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ON THE 

SCIENCE 

OF 









<D$mr 9 



EXPLANATORY AND DEMONSTRATIVE) 

Whic\\were Fixst Delivered,; 

AT VARIOUS PLACES IN tfEW- JERSEY? 

IN THE YEAR 1820. 

WITH A 

GLOSSARY AND SUPPLEMENT. 



BY DAVID YOUNG, 



MORRIS-TOWN, 

PRINTED FOR THE AtfTH0| ; 

By J. Mann. 

1821. 





^ 



District of New- Jersey, to wit: 

BE it remembered, that on the fourth 
^ day of December, in the forty sixth 
year of the Independence of the Uni- 
ted States of America, David Young, 
of the said District, hath deposited in 
this office, the title of a Book, the right whereof he- 
claims as Author, in the words following, to wit : 

" Lectures on the Science of Astronomy, explan- 
" atory and demonstrative, which were first deliv- 
er ered at various places in New-Jersey, in the year 
& one thousand eight hundred and twenty, with a 
* Glossary and Supplement. By David Young." 

In conformity to an Act of the Congress of the 
United States, entitled " An act for the encourage, 
ment of learning, by securing the copies of Maps, 
Charts and Books to the Authors and Proprietors of 
such copies, during the times therein mentioned ;" 
and also to the act entitled an "Act supplementa- 
ry to the Act, entitled an Act for the encouragement 
of learning, by securing the copies of Maps, Charts 
and Books to the authors and proprietors of such 
copies, during the times therein mentioned, and ex- 
tending the benefits thereof to the arts of designing, 
etching and engraving historical and other priats. 

Wm. Pennington, Clerk of the 
District of New- Jersey. 

JfJ/I/ 

,: <,' ¥3 



PREFACE, 



FOR several years past almost every person, 
among my numerous acquaintances, has manifest* 
cd a disposition to inquire into the Sublime mys- 
teries of Astronomy. The curiosity of people 
seems to have been sufficiently excited to jilt their 
mouths with interrogations on every occasion when 
I have been present. Questions of such a nature 
could not, however, be answered in a very trice, 
Most generally, neither I nor the inquirers have 
had sufficient leisure to attend to the subjects. ^ 

TJie primary object in view therefore in writing 
these Lectures, was that these reiterated questions 
might receive their final ansivers. I chose to de- 
liver them before classes formed for the purpose, 
in order thereby to abridge my labour in answer* 
ing the questions to every one. To promote, as 
far as I was able, the knowledge of Astronomy 
among my countrymen, was also a desirable ob- 
ject. 

When requested, by many of the audience, to 
publish the Lectures, I could not long refuse ; be- 
cause I supposed their publication might more ef- 
fectually and more extensively promote the accprn- 
plishment of my wishes. Frequent perusals will 
be more advantageous than a solitary hearing. 

If Piety and Religion may be promoted by 
the publication of small tracts; why may not the 
knowledge of Astronomy and the cause of Science 
in general, be advanced by similar means? 



iV JPEEFACE. 

I presume that no person will expect to find, 
these Lectures printed verbatim a$ they were de- 
livered. Revision is alio ays proper* and on the 
present occasion appeared so necessary that I 
have not been altogether negligent in that respect. 
But after all I shall be very far from challenging 
the critic to point out defects* 

Hanover, November 9, 182 V 



GLOSSARY. 



ALTITUDE, the distance above the horizon mea- 
sured on an azimuth circle. ' 

Amplitude, the distance of a celestial object, when 
rising, from the east point of the horizon, and 
when setting, from the west point of it. It is 
either north or south. 

Angle, the mutual inclination of two lines meeting 

in a point; a corner. . ■ 

Antipodes, [a local term] the inhabitants of the op- 

posite point of the earth's surface. 
Aphelion, that point »f a planet's orbit which is at 

the greatest distance from the sun. Flural, A- 

ApVgeT' that point of the moon's orbit which is at 
the greatest distance from the earth. This term 
is not unfrequently applied to the sun, to signdy 
that point in which he is farthest from the earth. 
Arc, a segment of a circle. 
Area, any open surface. . 

Aspect, a term applied to signify the situation or 
apparent distance of any two celestial bodies in 
the zodiac from each other. 
Asteroids, star-like bodies, a term of recent inven- 
tion, and applied to four small bodies lately dis- 
covered in the Solar System, between the orbits 
of Mars and Jupiter. 
Axis, a straight line,, real or imaginary, passing 
through the centrelof a body, on which it xmf 
revolve. Plural, Axes. 

A 2 



GLOSSARY. . 

4zimuth, the angle formed by the meridian and the 
vertical circle passing through the centre of any 
celestial object. 

Bissextile, a year consisting of 366 days, by add- 
ing a day to the month of February every fourth 
year. 

Centrifugal, flying off from the centre. 

Centripetal, inclining towards the centre. 

Circle, a line of uniform curvature, returning into 
itself, or ending where it began ; being in every 
part equally distant from the centre of the area 
which it includes. 

Circumference, the length of a circular line. 

Coma, a faint light surrounding the nucleus,, or sol- 
id body, of a comet. 

Concave., hollow, opposed to convex. 

Concavity, the internal surface of a hollow body. 

Conjunction, that aspect in which two celestial bo- 
dies in thfc zodiac have the same longitude. 

Constellation ; this term is applied to any assem- 
blage or cluster of neighbouring stars, which as- 
tronomers have classed together under one gene- 
ral name. 

Convex, rising in a spherical form, opposite to 
concave. 

Convexity, protuberance in a spherical form. 

Cycle, any certain period of time in which all the 
circumstances, to which the cycle has reference, 
regularly return. The most noted chronological 
cycles are the four following. 

1. The Solar Cycle, a period of 28 years, af- 
ter which the days of the months will fall on the 
same days of the week as i.a the same year of a: 
former cycle. 



GLOSSARY. 7 

2. The Metonic or Lunar Cycle, a period of 
19 years, after which the change, full and other 
phases of the moon, will return to the same days 
of the months as in the same year of a former 
cycle. 

3. The Roman Tndiction, a period of 15 
years, instituted by Constantine in A. D. 3I2 5 
and observed among the Romans as a period for 
collecting certain taxes. It was afterwards in- 
troduced into chronology. 

4. The Julian period, a cycle of 7980 years 
(arising from the multiplication of the three for- 
mer periods together) after which the years of 
the Solar Cycle, Lunar Cycle and Indiction, will 
all be the same as in the same vear of a former 

%j 

cycle of this period; provided the course of na- 
ture shall continue uninterrupted. The com- 
mencement of this period is of antem lindane 
date, for no later than the year B. C. 4713? 
could the other three cycles begin together. 

Data, such things as are known or granted, from 
which to reason. 

Declination? that are of the &i eridian passing 
through a celestial body, which is intercepted 
between it and the equator. 

Degree, [in mathematics] the 360th part of a cir- 
cle ; the integer by which the quantity of an an- 
gle is expressed. 

Density, hardness, closeness, compactness. 

Diameter, a line passing through the centre of the 
area of a circle, or through the centre of a globe, 
from side to side. 

Digit, a twelfth part of the apparent diameter of 
me sun or xaoon. 



§ CfliOSSAKY- 

fMsk the face of the sun, moon, or other planet, as 

it appears to the eye, 
Eccentricity, deviation from the centre, deviation 

from a circle. 
Eclivtic, the sun's apparent annual path through 

the heavens, the plane of the earth's orbit. 
Ellipsis, an oval figure, a figure approaching to a 

circle. 
Elongation, the angular distance of a planet from 

the sun. 
Epact, the excess of the Solar year above the Lu- 
nar; or it is (in the new style) the moon's age at 

the beginning of the year. 
Equation of time, the difference between apparent 

and mean Solar time. 
Equator, a great circle of the sphere, dividing it 

into northern and southern hemispheres. 
Focus, either of the two points where pins, or pegs, 

are fixed, in describing an ellipsis. Plural, foci. 
Friction, the resistance arising from the rubbing 

of one thing against another. 
Galaxy, a nebulous tract in the heavens; the 

Milky Way. 
Geocentric, having ithe earth for a centre; having 

the same centre as the earth. 
Globe, a sphere, a ball, a round body having all 

parts of its surface equally distant from its 

centre. 
Glossary, a dictionary of obscure or antiquated 

words. 
Goiden Number, the year of the Lunar Cycle. 
Heliocentric, having the sun for a centre. 
Hemisphere, half a sphere ; half a globe. 
Horizon } the line or circle that terminates our 



view; the circle which appears to divide the 
heavens and the earth. -r 

Inclination [in the mathematics] a tendency oi one 
line, or one plane, towards another. 

Latitude [in the heavens] is reckoned north and 
south from the ecliptic, as that on the earth is 
from the equator. 

Longitude is reckoned eastward from the first 
point of Aries quite round the heavens to the 
same point a^ain. 

Maximum, the utmost extent, the highest degree. 

Nadir, the point, in the heavens, which is directly 
under our feet. A local term. 

Nebulce. whitish spots in the heavens, caused by 
vast clusters of very distant stars. 

Nodes, points where the planetary orbits intersect 
the ecliptic. The point in which a planet passes 
the ecliptic from south to north is called the as- 
cending node, and that where it passes it from 
north to south is the descending node. 

Nucleus, the body, or solid part, of a comet. 

Oblate, flatted at the poles. 

Occupation, the time that a planet or star is hidden 

by the interposition of the moon. 
Opaque, obscure, dark, not transparent. 
Opposition, that aspect in which the difference of 
longitude of two bodies is 130 degrees, or half a 

circle. 
Orbit, the path in which a planet moves round the 

sun ; a circular path. 

Oval, a figure approaching to a circle; an ellipsis. 

Parallax, the difference between the true place of 

a celestial body, seen from the centre of the 

c^rth, and its apparent place seen from a spec- 



10 <GL0SSART» 

tator on the earth's surface. It is always equal 
to the angle at the body subtended by a semidw 
ameter of the earth terminating in the place of 
the observer. 

Parallel, extended in the same direction, always 
preserving the same distance, 

Penumbra, a faint or imperfect shade, observed in 
Solar eclipses, and occasioned by a partial inter- 
' ception of the sun's light. 

Perigee, that point in the moon's orbit which is 
nearest the earth. This term is also frequently 
used to signify that point in which the sun is 
nearest the earth. 

Perihelium, that point of a planet's orbit which is 
nearest to the sun. Plural, perihelia. 

Phenomenon, any appearance in the works of na- 
ture. Plural, phenomena. 

Plane, an even surface, a level area. 

Quartife, that aspect in which two bodies have 90 
degrees difference of longitude. 

Radius, the semi diameter of a circle. Plural, radii. 

Refraction, the variation of the rays of light from 
their direct course on entering obliquely into a 
different medium. 

Rotundity, roundness, sphericity. 

Satellite, a small planet revolving round a larger 
one ; a secondary planet. 

Secant, a right line drawn from the centre of a cir- 
cle, touching one extremity of an arc and con- 
tinued .until it meet the tangent which touches 
the other extremity of the arc. 

Segment, a part cut off from a circle by a line not 
passing through its centre; also a part cut off 
from a globe, in like manner, by a plane not 
passing through its centre. 



SL0S3ARY. 



11 



Sextile, that aspect where the difference of longi- 
tude of two bodies is 60 degrees. 

Sine a line (within a circle) dropped from one ex- 
tremity of an arc, and falling at right angles on 
the radius which touches the other extremity ot 

the arc. -, 

Sphere, a round body ; a globe, [see globe.J 
Sphericity, roundness, rotundity. 
Spheroid" a body approaching to the form of a 

snli^re 

Syzyffv ;' tills term is applied both to signify the 
conjunction and the opposition of a planet and 
the sun. It is however used chiefly m relation 
to the sun and moon. 

Taneent, a right line which touches a curve in one 
point, and is perpendicular to the radius of cur- 
vature. The tangent of an arc meets the secant 
of the same arc, and terminates at the junction. 

Transit, the passage of one of the heavenly bodies 
over another ; the passage of Mercury or V onus 
across the sun's disk. 

Trine, that aspect where two bodies are at the dis- 
tance of 120 degrees from each other. 

Zenith, that point in the heavens which is directly 
over our heads. A local term. 

Zodiac, an imaginary belt or girdle surrounding 
the heavens, extending so wide on both sides et 
the ecliptic as to include the orbits of all the 
planets. 



A TABLE 

Showing the Length of a Degree of Longitude &t 
every Degree of Latitude, from the Equator to 
the Poles, in English miles, 



tr En2f. 




1 

2 



69.50 

69.49 
69.46 



3 69.40 
69.S3 
69.24 



5 



6 69.12 

7 68.98 

8 68,82 

9 68.64 

10 68,44 

11 68.22 
12}67.98 

13 67-72 

14 67-44 

15 67.13 

16 66.81 

17 66.46 



18 

19 

20 
21 

22 
23 
24 
25 
26 

27 
28 

29 
30 



Eng. 

Miles 

66.10 

65.71 
65.31 
64.88 
64.44 
63-98 
63.49 
62.99 
62,47 
61.93 
61.36 
60.79 
60.19 



31 59.57 



32 
33 
34 



35 



58.94 

58.29 
57.62 

56.93 



,r 

■ pa 

f ft- 

\k 

; 37 

'38 

39 
40 
41 
42 
43 
144 
45 
46 

47 

48 

49 
50 
51 
52 
53 



Eng. 
Miles 
56.23 
55.51 

54,77 
54.01 

53.24 
52.45 
51,65 
50.83 

49*99 

49.14 

48.28 

47.40 

46.50J 

45.60' 

44.67 
43.74 

42.79 

41.83 



. 

54 
55 
56 

57 
58 

59 
!60 
61 
62 
63 
64 
65 
66 

67 

68 

69 
70 

71 



Eng.. 



p. 



s 

40.85 
39.86 
38.86 
37.85 
36.83 
35.80 
34*75 

33.69 
32,63 
31.55 
30.47 
29.37 
28.27 
27*16 
26.04 
24.91 
23.77 
22.63 



72 

73 

74 

75 

76 

77 

78 

79 

80 
81 
82 
83 
84 
85 
86 

87 
88 

89 



Eii£. 
Miles 

21.48 
20.32 
19.16 

17.99> 
16.81 
15.63 
14.45 
13.26 

12.07 
10.87 

9.67 
8.47 
7.26 
6.06 
4.85 
3.64 
2.43 
1.21 



The degrees of longitude vanish at the poles. 




INTRODUCTION, 



THILE the tumultuous world are eagerly 
f and almost incessantly employed in the 
necessary branches of agriculture, commerce and 
manufactures; occupied -in the various arts of peace 
and of war 3 engaged in the pursuits of worldly 
pleasures, of wealth, or of power; a variety of 
sublime objects, in a great measure, escape their 
attention. We are surrounded by objects most 
magniiicent, most stupendous; the visible Heavens 5 
incomprehensible in their dimensions, evincing, by 
the irrefragable argument of 7 their own existence, 
objects infinitely greater still; the Existence, the 
Eternity, the Ubiquity, the Omniscience and the 
Omnipotence of One JEHOVAH! 

A general acquaintance with the form, dimen- 
sions, motions, and relative situations of the earth 
and of the celestial bodies, has a tendency, opt 
only to divest the mind of many superstitions no- 
tions, but also to strengthen our faith in those more 
sublime and more important truths communicated 
to us by Revelation ; the immortality of the human 
soul, the apostacy of man from God, and the be- 
nevolence and compassion of the Infinite Sove- 
reign, as displayed in the Redemption or the world 
through Jesus Christ. Thus it elevates the mind 
infinitely above the highest possible attainments of 
any inferiour nature. 

I hope there are none, in this enlightened age 
and country, who doubt the possibility of the at- 

B 



* 



14 INTROBUCTION. 

iainment of this knowledge. Shall It be thought 
strange that mankind, considered as rational and 
immortal beings, should become acquainted with 
the form and dimensions of the earth, on which 
they exist? Shall it be deemed incredible that 
they should attain any knowledge of the distance of 
the nearest of the surrounding spheres? Is it not 
rather strange and unaccountable that such knowl- 
edge is not more general ? 

The progress which Astronomy has made is 
owing to the" indefatigable exertions of a very small 
proportion of mankind. That its advancement 
has been so slow, is because so few have been en- 
gaged in it; the great mass of men. having been 
occupied in a multiplicity of other concerns. But 
%vhy is it that in modern times, after discoveries so 
great and manifold have been made, so few attain 
any correct knowledge of this kind ? It is owing 
to many difficulties which lie in the way. The 
most formidable of these are the criminal ignor- 
ance, the kiveterate prejudice and the superstitious 
notions of mankind. Such are the dense clouds 
which still hang about the horizon and prevent the 
rays of Science. Happy for the present age, as 
well as auspicious for future generations, the clouds- 
begin to be dispersed ; the difficulties seem in many 
instances to give way, and we are cheered by the 
sanguine hope that Science and Truth will finally 
prevail. One very conspicuous cause of reforma- 
tion in this respect, which I would not fail to men- 
tion, is our enlightened Clergy; whom I would, oa 
every occasion, devoutly exhort to use the influence* 
they may possess, in removing superstition frera 
the minds of men. 



INTRODUCTION. 



15 



An exertion of the mind will be necessary in or- 
*ier to a thorough understanding of the subjects be- 
fore us. There are some problems, the solutions 
of which appear exceedingly difficult on a superfi- 
cial view, and have by many, in their ignorance 
and in their haste, been pronounced impossible; 
-which nevertheless have been truly solved by men 
who have paid strict attention to the subjects.— 
There are many persons whose studies are very 
few, except in relation to their secular concerns, 
and who never penetrate into the depths of philos- 
ophy or the heights of astronomy. It is to be ex- 
pected that such persons will be surprised at the 
declarations of others respecting these sublime sub- 
jects. What less than wonderful can we expect to 
meet with when we canvass, even to the extent of 
our own narrow capacities, the works of HIM 
whose presence fills immensity, and whose power 
and wisdom are infinite? 

With respect to the subjects now to be consid- 
ered, it would be a mere waste of time to consult 
the opinions of the learned among the ancients ; 
nor need we bring into view the various absurd 
opinions, arising from the combined influence of 
Ignorance, prejudice and superstition, which have 
so greatly prevailed among the unlearned until the 
present day. If truth be exhibited and maintained, 
the whole mass of errour must fall before the face 
#f it. 



LECTURE FIRST, 

in Illustration of the Figure and Motion oj 
' the Earth, together with those of the Celestial 
Bodies. 

5T appears to have been natural for mankind to 
consider the Earth as stationary, or at rest, and 
its general surface as a continued plane ot unknown 
extent : and although men of science have long since 
discovered that these things were not so, yet mese 
errors have been too deeply rooted in the mmas of 
others to be easily eradicated. Surprising as it may 
appear, there are, even in the present generation in 
our own country, very many who are strangers to 
the true form of the Earth, and who will allow it no 
motion whatever. It seems necessary, therefore, 
that these subjects should occupy a place in the 
commencement of these Lectures. 

Figure and motion I prefer attending to undei 
one head, rather than separately, because ot a cer- 
tain connexion existing between them, and because 
the former, in some respects, depends upon, and 
can only be explained by the latter. , 

The sun and the planets always present circular 
disks towards the earth ; for the planets are appar- 
ently so magnified by the telescope that their form 
can easily be observed. The sun and most of the 
planets have also, by means of spots on their disks 
which telescopes render visible, been observed to 
revolve about 'their axes in such a manner as to pre- 
sent different sides towards us at different tunes, 

B2 



1 



8 THE FtGURE ASTD MOTIOSf 



These two circumstances amount to an absolute 
proof that they are globular bodies. From hence 
we might very naturally infer that the form and 
motion of the earth are similar. But we are well 
supplied with arguments which are entirely con- 
elusive, and therefore need not resort to analogical 
inferences. I propose to prove?. 

First, that the figure of tke earth is nearl/ glob- 
ular, or spherical, and 

Secondly, that it is not a perfect sphere. 
Jl All men of erudition in the present age are 
agreed, not to give it as their opinion, but to declare 
it as a fact, that the figure of the earth is nearly 
spherical. This figure we shall prove, 

1. From the phenomena of the visible heavens 
seen from various parts of the earth. 

If the surface of the earth eenerallv fthat is ex- 
cepting those small inequalities of the land, called 
mountains, hills, ridges and vallies, which I shall 
all the while except) were an extended plane ; then 
the sun would rise and set at the same instant to all 
parts of this plane. Consequently the days or the 
nights would be of the same -'length- in every part of 
the world at any time of the year. They might be 
longer at one season and shorter at another, but 
they could not be longer at one place and shorter 
at another. The moon, the planets and the stars, 
supposing the surface of the earth to be a plane, 
would likewise rise and set, with respect to every 
nation, at one and the same instant. Let a~person 
travel east or west with a watch in good order, well 
regulated, and set right for the place from whence 
he starts. Let him also carry with him an account 
of the time of the rising and setting of the suj% 



©F THE EARTH ; &CT. 13 

moon, planets and stars, for every day, suited t& 
the latitude and horizon of the place from whence 
he sets out. Let him travel far enough to be con- 
vinced, say one, two or three thousand miles. He 
will find the time of the day at the places where 
he arrives to differ widely from that shown by his 
watch; and the time cf the rising* and setting of the 
luminaries of heaven will not correspond with his 
account according to his watch* Will any one say 
that his watch has become disordered? There is 
a way to determine whether this be the case or not. 
Let him return to the place from whence he set out 
and observe whether it be not right. A man may 
be informed, by an astronomer^ of an invisible e- 
clipse of the moon, which at some other place is t© 
be visible, for instance, at London. A correct 
statement may be given him of the day, hour and 
minute of the beginning, middle, end, and all other 
phenomena of the eclipse, both by his own meridi- 
an and also by that of London. He may procure 
two good watches, well regulated, and have them 
set by a person understanding astronomy, one to 
his own meridian, the other to that of London.— 
Thus equipped, he may sail to- London, observe 
the eclipse, and be convinced. With regard to 
the different length of the days and nights in dif- 
ferent latitudes, a man may convince himself with- 
out understanding mathematics. He may be at 
Savannah one twentieth of December and at Que- 
bec another, and observe ; or he may observe in 
any two places, whose difference of latitude is con- 
siderable, on any certain day, except about the 
equinoxes, in two different years. 

Now we have what amounts to all this. These 



<"i 



THE FIGUBJE AND MOTION 



things are well known by the abundant corres- 
pondence which is carried on between ail parts of 
the civilized and the civilizing world. A corres- 
pondent at London may inform that their longest 
days are 16 hours 25 minutes, and their shortest, 
7 h. 35 m. another at Edinburgh may state their 
longest at 17 h. 20 m. and their shortest at 6 h. 40 
m. °a third from the mouth of the River Amazon, 
or from the Island of Borneo, may write that their 
days and nights are always just twelve hours long; 
and who would pretend to disbelieve? A man 
may as well doubt the existence of London or Ed- 
inburgh or the River Amazon, or any other thing 
in nature that he has never seen. Who, then can 
believe the surface of the earth to be a flat extended 
plane, when in other parts of the world they see 
the sun or moon for hours after it is gone from our 
view, or before it rises to us ? and when in some 
countries they enjoy the full refulgence of noon ? 
while we have the cold, damp, gloomy, midnight 

hour ? - 

Having thus proved, in a manner altogether un- 
equivocal, that the surface of the earth-us not an 
extended plane; I purpose, before I dismiss the 
present argument, to prove that it is convex, like 
the surface of 'a globe or sphere. 

All the stars continually preserve the same situ- 
ation with respect to each other; on which account 
they have been called fixed stars, in order more 
effectually to distinguish them from the planets.— 
They are three minutes and fifty-six seconds earlier 
every night in their rising, setting or coming to the 
meridian, than they were on the preceeding night. 
Therefore lot a person observe, in the letter part tf 



OP THE EARTH, &C. 21 

the night, what conspicuous stars are on or verj 
near tbe meridian in its whole extent from the ze- 
nith to the horizon, both nortli and south, and tak& 
their apparent altitudes. Let him then travel due 
north or south; and every fifty or every hundred 
miles observe again the altitude of all those stars at 
the time when they come to the meridian; which 
will be earlier man at the time of his first observa- 
tion, according to the number of days which have 
intervened, at the rate of 3 minutes and 56 seconds 
for- each day, amounting in 60 days to 3 hours and 
56 minutes. Suppose he travel north, and the 
surface of the earth be a plane ; then the stars be- 
fore him near the horizon will be but little affected 
by his travel ; but little elevated above the horizon 
7nore than they were, seen from the place where he 
first observed "their altitudes; because his course is 
so nearly directed towards them. Those higher 
above the horizon will be more elevated, because 
their direction does not so nearly coincide with that 
in which the person is supposed to be moving,— 
Those -aear the zenith will be most affected of all; 
because their direction is at right angles with the 
motion of the person: so thatrbose which were but 
little north of the zenith will (if he go far enough) 
appear- south of it The stars on the meridian 
south of the zenith will appear to be depressed, m 
the same manner as those north of it will be appa- 
rently elevated; those nearest the zenith, the most 
affected in this respect, and those nearest the ho- 
rizon the least so. This idea can certainly be 
distinctly communicated. If you travel north, an 
object which was due east soon falls to the south; 
one which was north-east is less affected, but is 



THE FIGURE AND MOTION 

after a while (if you travel far enough) seen in the ' 
east; while an object which was due north remains 
due north siill, and will thus continue until you ar- 
rive at it. Thus the altitude of those stars on the 
meridian which are nearest the horizon, will be the 
least affected by travelling either north or south; 
and that of those nearest the zenith will be the most 
affected. But if the earth be of a globular form, 
X\\e effect will be very nearly equal with regard to 
every star on, or near, the meridian. I need add 
nothing further at present," except to inform you 
that the result of such experiments is well known, 
-and to advise those who may not be convinced by 
the united strength of this and the succeeding argu- 
ments, to make this experiment themselves. 

2. We shall prove the spherical hgure of the 
earth, in the second place, from the universal law 
of Gravitation. 

There is a certain principle, property? power or 
law of nature by which all separate bodies tend 
towards each other. By this principle, or Llw, all 
bodies of greater density than air, will fall to the 
earth, on whatever side of it they may be. By this 
principle, all bodies of greater density than water, 
will sink to the bottom of the water. The greater 
the density of a body is, the greater quantity of 
matter is contained in any certain magnitude; and 
consequently, as gravitation operates equally on all 
matter according to its real quantity, and without 
regard to its extent, it must operate more powerful- 
ly °on a common stone than upon the same dimen- 
sions of water, and on almost any other substance 
than upon the same measure of air; and as water 
and air are fluid, they easily admit other substai*. 



«p THE EAItTH, &C. 2 ' 3 

, a « -vV,irh are more powerfully drawn, Or attracted, 
to »£ SS By virtue of this prmcipK 
£S feLng from springs, ponds or lakes wdl 
^n and form channels in the lowest place, which 
Aev can find. By virtue of this power or law, ne 
u ace of "he ocefn is in every jW^gWJj; 
ta nt from the earth's cen re . Th, - gggg 
every particular pond or laKe. uy iN „„f fl „:H 
same principle, power or law, any quantity of fluid 
endreh detached from all other substances, would., 
by Utual attraction of its parts, -sum- form 
wv nearly spherical; and supposing it to be pe.- 
fectr a Trest, P and beyond the sphere of attraction 
of anv other matter whatever, its Hgure would be a 
St sphere. By the same law of nature the 
So PS of r^n, in their descent, assume nearly a 

6P ^mavE rationally conclude that the ear* 
U hTSme form; especially considering ^d the 
ereatest part of its surface is covered with water. 
She waters of all the oceans arc ^connected yg 
these connected waters wash every shore oi every 
comment and island; and that by their e^uanes 
fcey so nearly bisect even the largest portions pi 



S We" shall in the third place prove the spheric- 
al figure of the earth from its shadow m ecupses of 



the moon. 



It may 'be laid down as an axiom, that a body 
.hosfsLdow is always circular, from .whatever 
side the shadow may be cast upon anothe body^ 
must itself be a globe or sphere. Jh.s being the 
case with respect to the shadow of the earth, aW 
evidence of the earth's spherical figure. But W 



%4 THE FIGURE AND MOTION 

order to set this argument in the clearest light, and 
give it full weight, 1 must show that eclipses of the 
moon are occasioned by the snade of the earth; and 
in order clearly to demonstrate this, it will be neces- 
sary to prove that the moon is not a lucid body, 
shining by her own light, but opaque, reflecting 
the rays of the sun ; and again, in order for this, it 
will be needful to show that the moon is spherical, 
or, at least, that she presents a convex surface to- 
wards the earthy I must then attend to these three 
things in the retrograde order, and show -first that 
the form of the moon is globular, or at any rate, 
that the side which she presents towards the earth 
is hemispherical. 

If the moon were revolving in such a manner as 
to present different parts towards us at different 
times, and yet her disk were at all times circular, 
then her sphericity were evident; but she at all 
times presents to us the same part. Let us for a 
moment- take for granted the opacity or obscure- 
ness of the moon, which comes next to be proved, 
and we shall perceive that the manner in which 
the light of the sun comes on this side, and goes oif 
from it, can be explained, or accounted for, on no 
other hypothesis than that of its being a hemis- 
phere. With respect to -the form of the farther 
side of the moon, which is forever hidden from our 
view, that it is also a hemisphere does not admit 
of actual demonstration ; but if we consult analogy 
and the laws of nature, we may be convinced of 
the absurdity of any other supposition. Whoever 
believes it to be in the form of a cylinder, or of a 
c^ne, or of a prism or pyramid, or m any other 



-OF THE EARTH, &C. »J 

form more irregular and unnatural, ought not to 

8 Tcol S nowTln*he second place, to prove that 
J2Z is an obscure opaqUa ^/^^ 
by reflecting the Solar rays. Tins I shall do oy 

86 fSt ^S^Ssitude of light and darkness 
which we observe on the moon, cannot be exp-n- 
ed by supposing her to have a dark «nd a bngM 
Jde each of which is alternately turned towards 
usfb cause it is well known that the samej 
always towards us. This any one may observe 

"tl^^ moon shone by her own hide- > 
D endem lustre, she would always appear bright, 
Stme body should come between her and us, 
and thus obscure her partially or J^h m 

Thirdly The manner in which the light comes 
on audioes off, is altogether unaccountable by the 
?nterventk of 'a body'of any shape whatever • ; and 
nevfectly correspondent to that in which the light 
S'anyluminaiy P must appear to come on the side 
of a globe towards the observer, and g° f from £ 
when it is moved round him towards and from the 

lU1 FoSlv The position of the sun and moon 
with rlspe^t to the eWn, is always perfectly con- 
sistent with the position ol the light and daiknos 
on the moon. 

~h7^e7s^s^f OHo, ^oasserUthe 
mrth to he hollow and habitable within., x A» « 
perhaps the oddest, wildest, fmey g wUch the 
present age can boast. 



26 THE FIGUHE AND MOTION 

Finally. By the assistance of telescope?, astron- 
omers discover many of the irregularities of the 
moon, with which they are well acquainted, when 
they are some distance within the confines of the 
darkness: mountains and elevations lying in the 
regions of the twilight : volcanoes in the interiour 
parts of the darkness, which do not appear to 
move while the darkness passes off, as they would 
if they belonged to an intervening body which was 
passing by. 

Thus I have prepared the way to sIigw, as was 
proposed, that eclipses of the moon are caused by 
the shade of the earth. Having sufficiently proved 
that the moon shines only by reflecting the Solar 
rays, it immediately follows that she will cease to 
shine, even at her fully if those lays be intercepted 
by the intervention of any other body. We know 
that every opaque body, on which the sun shines, 
prevents those rays which strike itself; and occa- 
sions what we call a shade on the side of it opposite 
to the sun. Thus every planet has its shade 3 and 
as the moon is never eclipsed but when she is fuil ? 
that is, when in opposition to the sun, it is manifest 
enough that her eclipses are occasioned by the 
shade of the earth* 

Thus (he third argument which I have advanced 
to prove the spherical figure of the earth, may havg 
its full weight. The earth must be globular, be^ 
cause her shadow is always circular, when it a-> 
pears on the moon, whatever side may "be turned 
towards it. 

4. Several other considerations, on which we 
have not time to dwell, evince the same thing.. 
Tfcdeed, every circmnstance any way Gonnccted 



OF THE EAETH, &C. ~7 

fe tfe tfe fi-ure of tbe earth, furnishes unequivocal 
S deiS thS it is spherical. We might prove * 
PS dV of the horizon, which is perceptible from 
a y s allefevation, and which, if the earth's surface 
^■e, plane, could not be perceived from tne mm- 
S of he highest mountains, f e might prov e it 
by the appearance of ships at a distance on the o- 
ti„ ISly hidden by the convexity of the water: 
*%%£&&& voyages, ^»£$g* 
frenuent in modem times: by travels, whediei by 
L* or tfater: into all climates excepting very neai 
S^pol^ount, of which have been published 

Sn&ce, by the general ?%gg$&£S- 
kind with almost every region oi the earth ssmtace, 
Sh xkob bevond region, whether of ocean or of 
Sdfuntil it completes the circumference of the 



GLOBE. 



Now for a person to dispute the rotunduy ot the 
earth against 'such a weight of evidence as has been 
S2S, cafanot be less than folly and madness; 
ESS when we consider that there .s not one 
soPtary feet to support him in the wrong. 

II I now pass to the second general proposition, 
w!l Hwas to show that although the form of the 
earth and of the other planets is nearly spherical, 
yet that it is not a perfect sphere. 
■ Now that the figure of the earth is not a perfect 
Sphere, excepting the small inequahties before men-. 
f'.ned, can only be caused by her motion. We 
have shown that the planets revolve on their axes, 
which are imaginary lines pas sin g tnrougl then- 
centres. Such a motion is called a to^gj 
tion, because, by turning various parts of a planet 
to ana from the sun in their turn continually, it oc* 
mmms a constant succession of day and night. 



28 THE FIGUKE AND M0T30N 

We shall first show, under this head, that the 
earth has such a motion. 

Secondly, that such a motion would prevent her 
figure from being a perfect sphere. 

1. In the first place, that the earth revolves on 
her axis we might infer from analogy, it having 
been determined by observation that the other 
planets have such a motion. But not to put too 
much stress on analogy, though it seems in the 
present case to have considerable weight, I shall 
pass on. 

Secondly. It being certain that either the globe 
revolves daily on her axis, or that the sun, moon 
and stars perform a revolution daily around the 
earth, I shall prove the former by disproving the 
latter. 

And here, if it were possible for an Almighty 
arm to grow weary, I might draw an inference in 
my favour, from the eass with which the earth 
might be turned on her axis, in comparison with 
the labour which it would require to carry such a 
vast number of such huge globes through an extent 
ef space so inconceivable. But as nothing is hard 
with the Almighty which is in the nature of things 
possible, I shall argue only in the manner following, 

First, from the known laws of nature, 

Secondly, from the evident absurdities of a con- 
trary supposition, and 

Thirdly, from the total want of evidence on the 
opposite side of the question. 
• First. I shall argue from the known laws of na- 
ture. 

First, Gravitation. This we have previously 
mentioned. This is a known law : known by if» 



«p the EAivni, &e. ~ y 

feHKtatf operation. It is the operation of this law 
SSeSe. what we call the weight of borne,. 
This is often called the centripetal prce. 

4*ndl V ■ There is another law, called the cen, 
tr^Zl force, from its effect among the plane.s. 
T& that few by which a body, after having ie- 
SS an impulse; continues to *^g"?$* 
meet with no impediment, in a straight hi e, in it lie 
SSS and with the velocity cominumcated ^by 

^ 1 ^. -^ tknt if after the lapse oi ever bo 

the riiDu'se: bO utcu n> cutei i**v r 

£ i£5U of ages, it should strike ; any objea, 
the momentum with which it would stride womu be 
ti.e same with the impulse first given to it. x nis ^ 
that law without which you might throw a stone 
wu h all your strength, and it would proceed I no tar- 
ther than the length of your arm: without* mch a 
issuing from the barrel 01 a musket or tiie 

of the powder ceased to impel it: witnout vai.ch 
fall rP- Ldies would move nearly with an umlorm 
veS, and strike with no greater moment in 
tin their gravity. This law, as I sa.d, carries bo ; 
difis in a straight line, wltli undnnnusmng velocity, 
and forever, if they meet with no interruption or 
resistance. A body thrown mco the an doe, nc ; 
pursue a direct line, because the attraction ^ te 
Lth operates upon it; it does not move wiU an 

uniform velocity, because the air »«^g* ?& 

-*. \,,c **>t r»ftrtir>n^ in motion i<He\er, ue- 
jress: it dots act cOiAn.u- m iur"» ' 

Si either of these impediments .done is sutncicm 

tO 3tOD it. ■ „ .. tw^-c *»rv 

From the combined influence oi tneseU^xvc 
infe tiVQ things, . 



30 THE FIGURE AND MOTION 

First. We infer that one body may mt)ve round 
another; as when a small body, should be impelled 
in a direction at right angles with a larger one, the 
attraction of the larger body will turn the smaller 
one from the direct line, which it would otherwise 
pursue, and cause it to revolve in a circle or an 
ellipsis round itself. The attraction of the larger 
body, acting in a perpendicular direction to the 
motion of the smaller one, could have no tendency 
either to retard or to accelerate it. If by any law 
©f nature, a body, after being put in motion in a 
circle, would continue thus to'move voluntarily, or 
I of itself; then the attraction of the larger body 
might operate in drawing the smaller one nearer to 
itself. But this is not the case. If a gun barrel 
were uniformly curved, yet a ball discharged from 
it would not pursue a curve line. A body, there- 
fore, in motion round another has a tendency con- 
tinually to pursue a direct line: and this tendency 
perpetually balances the attraction of the bodv a- 
roimd which it revolves : so that, by the combined 
influence of these two laws, it would forever re- 
volve, unless some interruption should take place, 
This tendency to pursue a direct line, which would 
carry every revolving body away from the body- 
around which it revolves, has therefore been called 
the centrifugal force. 

If you fasten a weight to one end of a line, and, 
taking hold of the other end, set it to revolving (in 
a horizontal direction perhaps will be best) you 
will immediately perceive its tendency to fly off, or 
its centrifugal pendency. 

In the second place we infer that a heavier body 
will not move round £ lighter one; because the at- 



#P THE EARTH, &C. 51 

traction of the lighter body cannot balance the 
centrifugal force of the heavier one : but that the 
heavier body (if the disproportion be great) wilt, 
by virtue of its centrifugal tendency, nearly pursue 
its own direction, and, by its attraction, draw away 
the lighter body with it; because an inferiour pow- 
er cannot overcome a superiour. 

From the foregoing laws and the inferences we 
have drawn from 'them, it appears evident that the 
sun cannot move round the earth unless it be light- 
er than the earth. Now the real magnitude and 
distance of the sun can receive no attention in the 
present lecture; but it is needful, -in order to com- 
plete ray present argument, to show that it is much 
larger than the earth; which I will endeavour to 
do by a very plain and certain method. As I do 
not design to enter into the subject of dens' ty, I 
will for the present suppose that the sun may be so 
much less denVe rhan the earth, that if it be equal 
in size, still it may be enough lighter to revolve 
around it. What remains on this head is to show 
that it is much larger than the earth. 

On the supposition that the earth and the sun 
are equal in size, the apparent magnitude of the 
earth seen from the sun is equal io that of the sun 
seen from the earth ; or, in other words, the sun's 
horizontal parallax is just equal to his apparent 
semidiameter : so that if the centre of the sun were 
in the rational horizon, which is a great local circle 
in the heavens, whose plane passes through the 
centre of the earth, dividing the heavens and the 
earth into upper and lower hemispheres, the upper 
edge of his disk would be in the sensible horizon^ 
which is parallel to the former, and whose plane 






THE FIGUIIE AND MOTION 

- 



^ touches the surface of the earth at the place of tlie 
spectator. Therefore, to an observer at the equa- 
tor, the suits centre will be less than half the i\m* 
above the plane of the sensible horizon, and more 
than half the time below it; -although it muse hi 
just half the time above, and half below, the plane 
of the rational horizon.. This difference is the ef- 
fect of a parallax, which is occasioned by our dh-" 
tance from the earrhss centre. The horizovit a! 
parallax is an angle of depression, causing a lumi- 
nary to rise later and set earlier than otherwise k 
would do. The parallactic angle decreases as the 
distance increases; for the distance between the 
rational and the sensible horizons is just tlie semi- 
diameter ef the earth, which seen from a greater 
distance must evidently appear under a less aneie. 
But the sums horizontal parallax is jus! equal to 
his apparent semi diameter, on this "supposition ; 
because his semidiameter is here supposed to be 
just equal to that of the earth. The'sufrs apparent 
semidiameter is found by observation to be, at a 
mean rate, sixteen minutes of a degree; whicit 
turned into time, at the rate of 3 GO degrees to 24 
hours, amounts to one minute and four seconds by 
computation. This one minute and four seconds 
of time is the efiect which the sums horizontal par- 
allax would have on his rising and setting at rae 
equator, where otherwise he would always rise ana 

-—set at six o'clock, and the days and nights would 
be always equal. The day would be 4 minutes 
16 seconds shorter than the night. In our latitude., 
nearly 41 degrees north, the effect of such a par- 
allax on the sun's rising and setting, and on the- 
length of the day and night, would be increased by 



) 



OF THE EARTH, &C. 33 

one third, on account of the obliquity of the hori- 
zon to the equator j and could be perceived with as 
much advantage, because the very second of time 
when the sun would otherwise rise and set might 
be determined by calculation. But I hasten to 
state the argument which I would here raise, and 
to dismiss this part of the subject. 

The effect of such a parallax could easily be per- 
ceived by a well regulated clock • nay, the fourth 
part of it could certainly, and would unquestiona- 
bly have been perceived by the nice observations 
whkli have been made; whereas the true parallax 
is so small that its effect in this way is entirely im- 
perceptible. At any rate then the sun^s distance 
must be four times as great as such a supposition 
would make it, for the fourth part of such a paral- 
lax could and would have been perceived: and 
consequently he must be, at least, four times as 
large in diameter as the earth : and as the content 
of solid bodies, of a similar figure, is in proportion 
to the cubes of any of their corresponding dimen- 
sions, it results that the sun is at least 64 times as 
large as the earth, and therefore that it cannot re- 
volve around it. 

Thus I have proved the revolution of the eartn 
on her axis, by proving from the laws of nature 
that the sun does not move daily around the earth. 
Second I was in the next place to argue, in 
support of the earth's diurnal motion, from the evi- 
dent absurdities of the contrary supposition. 

If we deny the diurnal revolution of the earth, 
then we suppose, as was before observed, that the 
sun, moon, planets and stars move round the earth 
once every day; the absurdity of which hypothesis 
will appear from three considerations. 



84 THE FIGURE AND MOTION 

First, from the various times in which the Iieav- 
ens appear to revolve, seen from the different plan- 
its of this system'. To an observer on the sun, the 
heavens would appear to revolve once in 25 days, 
14 hours and 8 minutes; this hems the time of the 
sun's revolution on his axis by observation. Seen 
from Venus, the heavens appear to revolve in 23 
hours, 21 minutes and 7 seconds. Observed from 
Mars, the time of an apparent revolution of the 
heavens is 24 hours, 39 minutes and 21 . seconds. 
Seen from Jupiter, it is 9 hours, 55 minutes and 50 
seconds, and from Saturn, 10 hours, 16 minutes & 
19 seconds. It being impossible tor the svm, or 
the sideral heavens, to revolve around one planet 
in one period of time, and around other plane: 3 lu 
other different periods; we therefore conduce that 
it is only an apparent revolution of the Leavens, 
occasioned by the rotations of the planets on them 
axes. 

In the second place, it appears absurd that ona 
body should move round an imaginary line, con- 
ipeived to be drawn from another, and leave ; 
other body itself at a vast distance from the | >r. :e 
of its path or orbit; which is the case with most -.f 
the stars, if we admit the apparent revolution of the 
heavens to be real. 

Thirdly, on this supposition there are some very 
inconsistent motions among the planets. The sua 
revolves sometimes at a greater and sometimes at a 
less distance from the earth, as is evident from the 
difference observable in his apparent magmtutle, 
The planets vary vastly more in their distances, at 
Jeast some of them, as is evident Irom the same cir- 
cumstance. Some are nearer than the sun. at one 



OF TliE EAUTH, &C. « "5 

lime and more. distant at another. Some are near- 
est only when near their conjunction with the sun, 
others only about the time of their opposition to 
him. AH these circumstances, and others, which 
time forbids me to mention, are perfectly unac- 
countable on this supposition • while if we admit 
the diurnal motion of the earth, they are perfectly 
consistent with the laws of nature. 

Third. All the arguments which have been | 
urged in support of the earth's diurnal motion, 
must have their full weight, when we observe, in 
the third and last place, that there is a total want 
of evidence to the contrary. 

We have certainly found no evidence to the 
contrary in Nature; and k is equally certain that 
none can be found in Scripture. There can be no 
weight in those common and vulgar objections, 
that people cannot stand on their heads; that 
the waters would be spilled out of the wells, mill- 
ponds, &c. &c. They are too frivolous to be 
seriously attended to. We have not spoken of 
people standing on their heads, but of the Uni- 
versal Lata of Gravitation^ that principle which 
maintains the Oansu of nature; without which 
the waters of the great Deep might rush from their 
beds and drown us upon the heights of the Alps or 
the Appenines, the Alleghany or the Ancles; and 
without which we could as easily stand on our 
heads as on our feeL 

There are some who bring an objection from 
Scripture. " Joshua,' say they, 6 commanded the 
sun anil moon to stand still ; and how could this 
have been proper if the sun did not run?" I an- 
swer. That was the only proper manner in whisk 



36 THE FIGURE AND MOTION 

he could speak on the occasion. With respect t© 
the earth, the sun, moon and stars appear to run ; 
and who is there, even in modern times, that does 
not, in all bis ordinary discourse, speak as if the 
earth were standing still, and the luminaries of hea- 
ven revolving daily around us? A person who 
so strenuously adheres to. the literal signification 
of ever} 7 expression he may find used in Scripture, 
must renounce either the Scriptures or his reason. 
Will he suppose that he must hate his father and 
mother, and his own life, in order to he a worthy 
disciple of the Lord Jesus, because, according to 
the literal sense of the words, Christ has said what 
amounts to this ? Must he not renounce his reason 
in order to believe such gross absurdities and such 
palpable contradictions as are to be found in the 
Bible; or else reject the Bible altogether as being 
repugnant to reason ? How much better to " show 
the reason of a man," and understand onlv what 
was intended to be understood ! The Israelites 
w r anted longer time, on a certain day, to pursue 
their enemies and complete their victory. The 
Lord w^as pleased to grant this thing. Joshua, 
influenced by the Holy Spirit, bade the sun and 
moon stand still 5 and they stood still ! He made 
use of common language, in the foundation of 
which the earth is always considered as at rest, 
and therefore his expressions can be no evidence 
whatever respecting any point in astronomy. 

Thus I have proved the diurnal motion of the 
earth (which was the first thing proposed under 
the second general head) from the known laws of 
nature; from the absurdities into which a contrary 
supposition would involve us ; and from the total 
want of evidence to the contrary. 



OF THE EARTH, &€. 37 

2. The next proposition was to show that such 
fe motion would prevent the figure of the earth 
from being a perfect sphere. 

I observed, in the former part of this lecture, 
that, by virtue of the principle of gravitation, any 
quantity of fluid, entirely detached from all other 
substances, perfectly at rest and beyond the sphere 
of attraction of any other matter whatever, would 
assume the figure of a perfect sphere. Let us now 
suppose this "body of fluid, after assuming such a 
figure, should be set to revolving on a straight line 
passing through its centre. Such a motion would 
occasion a centrifugal force. Every particle of the 
fluid, at any distance from the line or axis on winch 
the body would revolve, would have a tendency to 
recede farther from it: and the farther the situation 
•of any particle might be from this line, the greater 
would be its tendency to recede from it. In conse- 
quence of this, its diameter in the direction of its 
axis would suffer a diminution, while in any direc- 
tion perpendicular to it, it would be increased. — 
Thus, by reason of this motion; it would deviate 
from a sphere, and assume the form of an oblate 
spheroid. This then is the true figure of the earth. 
I might further observe that, by the actual meas- 
urement of a degree of the meridian in different 
latitudes, the spheroidal figure of the earth has 
been reduced to a mathematical demonstration: 
and not only so, but it has been ascertained that 
the polar diameter falls short of the equatorial 
diameter 34 miles. 

I do not suppose that the earth has assumed this 
figure; but that the Creator gave it such a figure 
as should correspond to the motion which he had 

D 



$8 THE FIGURE AN© MOTION &C. 

communicated, or intended to communicate to it. 
For if it had been originally formed a perfect 
sphere, and there had been land situated about 
the equator and the poles, as well as elsewhere, 
with about the same elevation above the surface of 
the water with which we now find it, and no 
change had since taken place except such as would 
be produced by its motion ; we should now expect 
to find no land in the equatorial regions, and 
mountains about the poles elevated seventeen 
miles above the level of the ocean. 

The figures of those celestial bodies also, whicb 
have a similar rotation on their axes, are more or 
less oblate, in proportion to their magnitudes and 
the velocity of their rotations. 



V 




LECTURE SECOND. 

fke causes of the various Phenomena of the Visi* 
hie Heavens explained. 

AVING, in the preceding Lecture, proved, 
jjjbl among other matters, the diurnal motion of 
the earth and of the other planets; we have now a 
solid foundation on which to proceed to the explan- 
ation of the various appearances which we observe 
in the surrounding heavens. 

All the luminaries which nightly besprinkle the 
firmament, with the exception of a few, are called 
stars 5 and having, throughout all generations, re- 
mained very nearly in the same situation with res- 
pect to each other, have, from this circumstance, 
obtained the appellation of fixed stars. A desul- 
tory observation of the heavens is sufficient to dis- 
cover that there is a motion among a few of the lu- 
minaries, by which they continually vary their 
positions. These have on this account been called 
wandering stars, or planets. The phenomena 
which we behold are at once a decisive proof that 
the planets have another and a different motioa 
from that which was proved in the former lecture ; 
amotion by which they change their places with 
regard to space; and this motion when explained, 
will account for the phenomena. 

I shall in the first place shew that the planets 
revolve around the sun. Secondly, shew the man- 
ner of this motion, and the phenomena resulting 
from it. Thirdly, 1 shall attend to the naotioAS 
and phenomena of the moon. 



40 THE VARIOUS PHENOMENA 

I. The first proposition was to she,w that the 
planets niove around the sun; which motion we 
shall call their annual revolution. 

All the planets are found by observation to per* 
form revolutions around the sun. They are seen 
on every side of the sun in the direction of their 
motions. The paths in which the planets move 
round the sun are called their orbits ; and every 
planet is observed to pass between the sun and all 
the stars in or near the plane of its orbit, or path* 
We find that the fixed stars rise and set three min- 
utes and fifty-six seconds earlier every night than 
they rose and set on the preceding night, amount- 
ing in a year to one apparent daily revolution more 
than the sun apparently performs ; and it is evident 
that such mast be the effect of an annual revolution 
of the earth from west to east. If the earth's rev-' 
olution on her axis were stopped, and in this situa- 
tion,, she were carried once round the sun from 
west to east; the sun would then appear to us to 
perform a revolution round the earth the same way y 
which would not be the case with the stars, because 
they are not included in the earth's orbit, but are 
far beyond the confines of the system of the sun and 
planets. Now the effect of the earth's annual rev- 
olution cannot be destroyed by her diurnal revolu- 
tion ; it must therefore occasion a diminution of 
one from the number of apparent daily revolutions 
of the sun from east to west, which would other- 
wise be produced every year by her revolution on 
ber axis. 

It might be urged that although neither the sua 
nor the stars go daily around the earth, yet that an 
annual motion, either of the sun eastwardly or «rf 



OF THE VISIBLE HEAVENS. 4L 

the stars westwardly, would account for this accel- 
eration of the stars in their apparent daily revolu- 
tion. , . ., , • i 
Such a supposition is inadmissible ; inasmuch 

as we have proved in the preceding lecture that 
the sun cannot go round the earth at all according 
to the laws of nature, it being much larger than 
Hie earth ; and inasmuch as the earth, with regard 
to most of the stars is at a vast distance from the 
plan of their supposed orbits. But even li the sup- 
position could be admitted, that the stars perform 
an annual revolution round the axis of the eaitn 
Conceived to be produced or extended north and 
south through the planes of their apparent annual 
orbits ; we 'should have as much reason to suppose 
that these same stars perform a revolution rcunu 
Jupiter in a period almost twelve times as long, and 
on an axis some what different in its direction ; at 
least the inhabitants of that planet would have as 
TOod.reason to suppose so. No two planets would 
be found to agree as to the time of the penormance 
of such a revolution; therefore it must pass for an 
absurdity. Besides, the earth, and every planet, 
must go round the sun, in order to acquire a centri- 
fugal force sufficient to balance the sun's attraction. 
II. The next thing proposed is to show the 
manner of their motions, and the phenomena re- 
sulting from it. ... 
Here I would make a few general observations, 

and afterwards be more particular. 

1. The planets do not move in circles, but m 
orbits more or less elliptical, having the sun in one 
focus of their respective orbits ; so that every plan- 
et is nearer the sun in one point of its orbit iha» i|t 

D 2 



42 "The various phenomena 

any other, which point is called its perihelium, and 
in the opposite point the planet is at its greatest 
distance from the sun, called its aphelion. 

2. The planets do not all move with the same 
velocity in their respective orbits. Those farther* 
from the sun move slower, and those at a less dis- 
tance have swifter motions. 

3. The motion of any particular planet is not 
uniform. Every planet's motion is swiftest in its 
perihelium and slowest in its aphelion. 

4. The orbits of all the planets lie in different 
planes. The orbit of the earth is called the eclip- 
tic. The planes of the orbits of all the other plan- 
ets intersect the plane of the ecliptic, making small 
angles with it, and therefore one half of the orbit of 
every planet lies on the north side of the ecliptic, 
and the other half on the south side. The points 
where the orbits of the planets intersect the ecliptic 
are called their nodes ; that in which a planet cros- 
ses the ecliptic from south to north is called its as- 
cending node, and where it crosses from north to 
south is the decending node. The nodes of the 
different planets lie in various parts of the ecliptic. 

5. The axes of the different planets are variously 
inclined to the planes of their respective orbits, and 
to that of the ecliptic. 

These several things have all been determined, 
together with the particulars relating to them, by 
the nice observations of astronomers ; and as they 
all serve to explain certain phenomena, so by the 
phenomena their own truth is confirmed. 

6. From the principles of gravitation and cen- 
trifugal force, we infer that the velocity of a planet 
in its orbit must be proportioned to its distance froa* 



OS" THE VISIBLE HEAVENS. 43 

the sun, in such a manner that vhe two '&&*& 
be equal ; and therefore the longer a planet takes 
to perform its revolution round the sun the greater 
is its distance from the sun, and the contrary — 
Thus we discover the order of the planets ra the 
system to be as follows ; the first or nearest toe 
sun is Mercury, 2 Venus, 3 the earth, 4 Mars, 3 
Vesta, 6 Juno, 7 Ceres, 8 Pallas, 9 Jupiter, 10 bat- 
urn, 1 1 Herschel. Mercury and Venus, lying 
nearer the sun than the earth does, are cahed ime- 
riour planets. They change their appearance, wax- 
in* and waning like the moon ; being opaque bo- 
dies, and shining only by reflecting tne Solar rays 
as is the case with all the planets. All the otaer 
planets are farther from the sun than tne earth, and 
are therefore called superiour planets. Tnese^ do 
not change their appearance like the imenour plan- 
ets, because their enlightened side is turned so 
nearlv towards us at all times. 

7 "The inferiour planets, being situated nearer 
the sun than the earth is, and moving sooner round 
him, may sometimes be in conjunction with the 
sun seen from the earth, when they are beyond the 
sun in the most distant part of their orbits; which 
is called their superiour conjunction: and at other 
times they may be in conjunction on this side oi 
the sun in the nearest part of their orbits; whicn is 
called their inferiour conjunction: but they can 
never come in opposition to the sun. 1 he supe- 
riour planets are sometimes in conjunction with 
respect to the sun and sometimes in opposition, 
but when in conjunction they are far beyond it. 

8. The real motions of all the planets are from 
west to east around the sun. The apparent mo- 



44 «rHE VARIOUS PHENOMENA 

tion of an inferionr planet is always retrograde 
or from east to west, about the time of its inferiour 
conjunction; that of a superiour planet, about the 
time of its opposition. 

Having made these few general observations re- 
specting the planets, I shall now be a little more 
particular. 

1. The Sun Js a vast globe near the centre of 
the Solar System, around which all the planets 
and comets revolve, and from which they derive 
their light and heat. The sun has a very slow mo- 
tion round the centre of gravity of the whole sys- 
tem, which is near his own centre. His motion is 
very irregular, on account of the number of the 
planets by whose attraction he is thus affected. 
U ere it not for this motion the sun would be too 
easily drawn away from his station by a balance of 
attraction ofjhe planets, which is sometimes con- 
siderable. The sun's motion, however, is not sub- 
ject. to the same law or rule to which the motions 
of the planets are subject, but on the contrary he 
must move slowly around the centre of gravity 
because he is near it, or otherwise he would bv his 
centrifugal force be carried away and the svstem 
would be deranged. By observing the spots on 
his surface, astronomers have found that the sun 
revolves on his. axis once in 25 days, 14 hours and 
8 minutes. 

2. The nearest planet to the sun is Mercury, 
which performs a revolution round the sun from 
•nny star to the same again, or what is called a sidr- 
era] revolution, in 87 days, 23 hours, 15 minutes 
and 44 seconds. The orbit of Mercurv is more 
.elliptical or eccentric than that ,of any other of the 






OF THE VISIBLE HEAVE> T Sv 45 

leven first discovered planets, and is inclined to 
the ecliptic in an angle of seven degrees ; which,!* 
also a greater inclination than the oroit of any oth- 
er of the seven has. Mercury is so smal and so 
near the sun (being never more tnan about 2b de- 
grees distant from him) that be is seldom observed. 
He moves, at a mean rate, either from his imeriour 
or his superiour conjunction to the same again m 
115 days, 21 hours, 3 minutes and 34 seconds; 
which is almost 28 days longer than he takes to 
make a revolution round the sun, owing to tne dis- 
tance which the earth advances in tlie mean time. 
If the orbit of Mercury lay in the plane of the 
ecliptic, he would, at every in feriour conjunction, 
pari between the centre of the sun and the earth s 
centre; and might be seen like a dark spot passing 
over the suns disk. Such a phenomenon is called 
a transit. The same observation will also apply 
to Venus, which is likewise an inferiour planet.— 
A transit will take place when either Mercury or 
Venus comes to its inferiour conjunction at, or very 
near, either of its nodes; but at all other turn s the 
planet's distance from the plane of the ecliptic will 
be so great, either north or south, that it will pass 
the conjunction without coming between the earth 
and any part of the sun's disk. Mercury's last 
transit happened November 11th, 1815, invisible 
here; the next will take place November 4th, 
1822, at half past 9 o'clock in the evening, also 
invisible. The time of his revolution on his axis 
has not yet been determined. 

3. Venus is the next planet in the order of the 
system. Revolving within the earth's orbit, she is 
therefore called an inferiour planet. Her sideral 



46 THE VARIOUS PHENOMENA 

revolution is performed in 224 days, 16 hours an* 
49 minutes; and she goes from one infer iour con- 
junction to another,, at a mean rate, in 583 days, 
22 hours, 5 minutes and 23 seconds. Her orbit is 
less eccentric than any other of the planetary or- 
bits, and is inclined to the ecliptic in an angle of 3 
degrees, 23 minutes and 33 seconds. There was 
a transit of Venus across the sun's disk in the year 
1761, and another in 1769* The next will take 
place in the year 1874, beginning in the evening of 
the 8th of December and ending on the morning 
of the 9th, therefore invisible in America. The 
greatest elongation (or angular distance) of Venus 
from the sun, is about 48 degrees. When she i» 
east of the sun, she sets in the evening and is called 
■evening star ; and when she is west of the sun, she 
rises before him in the morning and is called morn- 
ing star. 

4. The earth (which we inhabit) is the third 
planet in the order of the system. The earth's or- 
bit is the ecliptic, in the plane of which the earth 
and the sun always are. If the axis of the earth 
were perpendicular to her orbit, the sun would be 
always on the equator, and would always rise and 
set at six o'clock to every part of the world, and 
there would be no vicissitude of seasons, such as 
spring, summer, autumn and winter. But her axis 
is at present (1 820) inclined to the plane of her or- 
bit in an angle of 23 degrees, 27 minutes and 46 
seconds, subject to a diminution of 52 seconds in a 
century. From this inclination it evidently results 
that one end of her axis, or one of her poles, must 
be turned more towards the sun in one part of her 
orbit, and the other end, or pole, turned more t&» 



$F THE VISIBLE HEAVENS, 4/ 

^vards him in the other part of her orbit. This 
sufficiently explains the phenomenon of the sun's 
declination north and south from the equator, the 
maximum, or greatest extent, of which is always 
equal to the inclination of the earth's axis to the 
ecliptic. This also accounts for the change of sea- 
sons; for although we are not obliged to believe 
the sun to be a body of Are, yet it is very certain 
that heat is produced by his rays, and that the de- 
gree of heat produced will, generally speaking, be 
greater or less, in proportion to the less or greater 
obliquity with which the rays of light strike the 
surface of the earth ; because when the obliquity 
is greater, fewer rays will strike on every square 
mile, or everv acre or foot of land. 

Another circumstance, claiming attention in this 
place, is the variation in the length of the days and 
nights in northern and southern latitudes, whereas 
at the equator there is no variation. 

It is not difficult to conceive that the horizon of 
that place on the equator and on the same meridian 
with us, intersects our horizon in the east and west 
points; and that the northern half of it is elevated 
above ours and passes through the north pole, and 
the southern part depressed below ours, passing 
through the south pole. Now it is plain that if the 
sun decline from the equator towards the north, he 
must cross the equatorial horizon after he rises 
above ours, and again before he sets to us; conse- 
quently our day must be longer than twelve hours. 
The hour of the day is the same here as at any 
other place on the same meridian, but the sun ri- 
ses earlier and sets later than at the equator, when 
his declination is north. It will be perceived that 



48 THE VARIOUS PHENOMENA 

the south declination of the sun would have the 
contrary effect ; and that the whole would be in- 
verted with respect to a place in the southern 
hemisphere; and that the circumstances are the 
same with regard to any other meridian whatever; 
and that the effect of the latitude of;the place and 
of the declination of the sun, in this respect, will- 
be more or less, in proportion to the greater or less 
latitude and declination. It is principally owing 
to the great length of the days (the heat having; 
longer time to accumulate) that it is found to be 
nearly as warm at a considerable distance from 
the equator, in summer, as it is at the equator. 

One more circumstance demands explanation 
here. At the poles of the earth it is six months 
dav and six months nicdit. 

With respect to either pole, the equator is in the 
horizon. When, therefore, the sun crosses the e- 
quator he rises to one pole and sets from the other. 
When he is visible, at either pole, he apparently 
revolves continually in aiesser circle parallel to the 
horizon, rising gradually higher and higher above 
it, until he reaches the maximum of declination, 
and then sinking lower and lower until, arriving at 
the equator, he sinks below the horizon! The sun 
shines nearly eight days longer at the north pole 
than- at the south pole, on account of the earth's 
unequal motion in her orbit, and the situation of 
Jier aphelion. 

The equation of time arises partly from the same 
cause, and partly jrom the inclination of the eclip- 
tic to the equator. We shall now proceed to the 
superiour planets. 

5. The fourth planet in order from the sun is 
JMars. He finishes his revolution round the sun in 



OF "TITE VISIBLE HEAvi^^o* 



4$ 



68G days, 23 hours, 30 minutes and 39 seconds; so 
that his year is almost as long as two of ours. The 
earth goes round the sun in less time than any of 
the superiour planets, and therefore brings them 
sometimes in conjunction with the sun, and at oth- 
er times in opposition to him. After leaving Mars 
at one of his oppositions, the earth overtakes him 
again at another, in 779 days, 22 hours, 28 minutes 
and 17 seconds, at a mean rate. The orbit of Mars 
is more eccentric than that of any other of the ori- 
ginal planets, except that of Mercury. Its inclina- 
tion to the ecliptic is i degree and 51 minutes. , 
There is one phenomenon of Mars worthy ot 
attention. Although he appears very small m 
general; yet there are times when he smnes with 
extraordinary brilliancy. In order to explain this 
circumstance, I would observe that it can only oc- 
cur about che time of his opposition to the sun ; at 
which time he is nearer the earth than at his con- 
junction, by the whole diameter of the earth's orbit, 
and nearer, by the semidiameter of it, than his 
mean distance. This must occasion a vast differ- 
ence in the appearance of Mars, considering that 
he is the next'planet above the earth in the system, 
and that therefore the diameter of his orbit does 
not, by a very great proportion, exceed that oi the 
earth. Venus, the next planet inferiour to the 
earth, would shine much brighter at her -infenour 
conjunction than at any other time, on account oi 
her proximitv, were it not I hat she is lost m the 
Solar rays, and that her dark side is also turned 
towards us. The earth shines vastly brighter to 
{ Venus at such a time than at any other. Bu 
there is a great difference between one opposit* 



50 "IlfE VARIOUS PHEIxOMENA 

of Mars and another*- in regard to his lustre. One 
is much more extraordinary than another in this 
respect. What can account for this ? — Nothing but 
the great eccentricity of his orbit. That the orbit 
of Mars is very eccentric, is evident from his une- 
qual motion; on account of which he is frequently 
brought to his conjunction or opposition sooner or 
later than the mean time by more than twenty 
days. When therefore Mars is in his perihelium^ 
at the time of his opposition, it will be the most ex- 
traordinary, and when he is in his aphelion at such 
a time, it will be the least so. The opposition of 
Mais in the summer of 1813 was very remarkable, 
The three nexU in the autumn of 1815, in Decem- 
ber of 181/ and January of 1820, continued to be 
less and less so; and that which is to take place in 
February, 1822, will be the least observable of all, 
Those which will happen in 1830, and 184$ will 
both be worth v of notice. 

6, The fifth, sixth, seventh and eighth planets 
in the system, are Vesta, Juno, Ceres 'and Pallas. 
These are very small planets, and have all been 
discovered since the commencement of the present 
century. They have obtained the general appel- 
lation of asteroids. Dr. Gibers discovered Vesta 
on the 29th of March, 1807. Its revolution round 
the sun rs performed in about 1155 days, or three 
years and two months. Mr. Harding discovered 
Juno, September 1st, 1 804. Her revolution is per- 
formed in about 1589 days, or four years and four 
months. Ceres was discovered by M. Piazzi, Jan- 
uary 1st, 1801. The revolution of this planet is 
completed in iGSl days, 12 hours and 9 minutes. 
On the 28th ofMarcfe, 1802, Dr. Olbers discover- 






Q-P THE VISIBLE HEAVENS. 51 

«d Pallas, which completes a revolution in 1703 
days, 16 hours and 48 minutes. 

The comparative distances of the old planets , 
from the sun had long been known, and their regu- 
larity, except between the orbits of Mars and su- 
pper (where there seemed too wide a space unoc- 
cupied induced some astronomers to believe tnat 
another planet might be discovered in tins region. 
The discovery of Ceres greatly strengthened this 
conjecture: but the opinion which it seemed to es- 
tablish, respecting the uniformity of the system 
was completely overturned by the discovery of 
Pallas and Juno. Dr. Olbers, however imagined 
that these small celestial bodies were only fragments 
ofalareer planet, once existing in those regions, 
which had been burst assunder by some internal 
convulsion-, and that other fragments mignt yet 
be discovered. He also conceived the mea that, 
although their orbits are differently inchned to the 
ecliptic, yet, as they all must have diverged from 
the same point at first, so they must have two 
common points of reunion, or two nodes in oppo- 
site points of the heavens, through which ah oi 
them must sooner or later pass. One o. . these 
points was found to be in Virgo and the other m 
Pisces; and it was actually in the latter 01 these 
points that Mr. Harding discovered Juno. W ith 
a view, therefore, to discover other fragments, Dr. 
Oibers observed, thrice a year, all the little stars 
about those points, Until his labour was crownea 
with success in the discovery of Vesta. Such cir- 
cumstances, I think, render the probability ot such 
an explosion very great. 

Before I proceed I beg leave to state that, accoiv 



52 THE VARIOUS PHENOMENA 

ding to an opinion which has begun to prevail 
among philosophers, those meteoric stones, which 
have fallen to the earth in so many instances, and 
concerning the origin of which there have been so 
many and so inconsistent opinions among mankind, 
are some of the smaller fragments of the once ex- 
isting planet. It is not found difficult to believe 
that an explosive force sufficient to throw off the 
larger masses to such' a distance as not to be drawn 
together again by their mutual attraction, might 
send out thousands of smaller fragments with such 
violence that they would proceed (so to speak) 
beyond the sphere of the attraction of the larger 
masses, and be found in almost every part of the 
system. Many of these small fragments might fall 
immediately to the sun, or light on some of the 
planets ; but much the greater number would very 
probably continue, for many ages, to revolve about 
the sun or some planet. This depends upon the 
direction of their respective impulses in relation to 
the system. Those revolving round the sun, from 
the interference of their paths with the planetary 
orbits, might sometimes come in contact with plan- 
ets. Those circulating round planets might, from 
the resistance with which they meet, even in pass- 
ing through the higher regions of the atmospheres, 
be so retarded in their motions as to fall* What 
other theory can account for bodies of such weight 
being at such a height from the earth as these are 
seen to descend from? What other theory can 
account for the velocity with which they move 
sometimes in a direction nearly horizontal? 

Time forbids me to dwell longer on this subject. 
Persons who wish to pursue it are referred to the 



CP THE VISIBLE HEAVENS. «*» 

New Edinburgh Encyclopedia, where they will 
fend it treated at large. _ gg 

7 The ninth planet is Jupiter, ric .» 

8S for from the sun as the earth, assent horn 

he time of his annual period, which is 4o. da>s 

1 1 Houm mid 51 m mutes, or nearly 12 yems. as 

the riity of r-ht which the planets receive from 

' «s .lavs 21 hours, 14 minutes and lo seconus. 
^Sc hation of his'orbit to the ecliptic » anan- 
X of 1 deoree, 18 minutes and 51 seconas, dimm- 
imnt at the rate of 22 seconds in a century . 
"'jailer is attended by four satellites « moenj 
Uich revolve around him at different 4istan.e» 
i; ^ rent times and are carried along with 
and in different times, ai Dlanets, or 

him around the sun. 1 heseSv.cc bm . j 

satellites, are easily seen by ^^^ffi 
artd I have heard a person asscn that tliey « 
Je seen about the time of Jupiter* opposition , iu, 

° U V U tc:SnTSl higher in the system, we ar ; 

riveai Si, lire **W : %££&£, 

the sim is nearly twice as great as that oi J up mr, 

s revolution being performed in *##"*£ 

half vears. Saturn comes to his o P po> tion once n. 

' 2rt W 2 hours, 1 1 minutes and 24 seconds.— 

T^e chnation"? 'his orbit to the eclipse is 2 e 

grees, 29 minutes and 38 secon ds Sat*m has , 

• satellites, or moons, and is also surrounded ^ 

vast ring; the plane of which forms an an^.c «M 

J'.« >j 



i THE VARIOUS PHENOMENA 

the plane of the ecliptic of about 30 degrees. The 
orbits .of the six first satellites appear to be in the 
plane of the ring, but the seventh evidently varies 
irom it. The ring is a singular curiosity and mav 
be seen by an, ordinary telescope. 

9. The eleventh planet, and the one most re- 
mote from the sun of any yet known, is HerscbeJ ; 
so called in honour of Mr. William HerscheL by 
.whom k was discovered on the 13th of March* 
1781. ft is twice as far from the sun as Saturn, 
and nineteen times the distance of the earth. The 
light, therefore, which they receive from the sun is 
only one 360th part of the quantity which we re- 
ceiv% yet, according to modern philosophers, it 
is about 250 times as much as our full moon affords 

U l> ?J^ C ^' * su PP ose ? is sufficient for every purpose 
of life. The degree of their heat probably depends,, 
in a great measure, upon the density of their at- 
mosphere; and who knows but this mav, in some 
degree, also affect their light ? Herschei performs 
his revolution in 83 years, 150 days, and 18 hours, 
and is in opposition to the sun once in 369 davs, 
16 hours, 33 minutes and 36 seconds. The incli- 
nation of his orbit to the ecliptic is 46 minutes and 
20 seconds. This planet is accompanied by six 
secondary planets, or moons. All these move in a 
direction nearly perpendicular to the orbit of" the 
primary, and contrary to the order of the signs. 

Thus, to use, with a little alteration, the words 
of a justly celebrated female writer, we have ar- 
rived 

4 ' At tfce dim ver^e, the suburbs oTjhe system, 
» nere cheerless' Herschei, 'midst his wat'ry moons, 
•••••. majestic sits 

in gloomy grandeur, }\ke an exiiM queen 
Amongst her weeping handmaids.' 1 



OF THE VISIBLE HEAVENc, -53 

111. From this lofty pinnacle we must now de- 
scend, as was proposed, to take a view of that sat- 
ellite which accompanies the earth, and which we. 
rail the mom. Here I shall ohserve some order in 
attending to the principal circumstances which af- 
fect the moon's motion and produce the phenomena 
which we behold. 

1. The moon moves from west to east around 
the earth, as the earth does around the sun, though 
not in the same plane. She appears to move from 
east to west, because the revolution of the earth on 
her axis is performed in so much less time than 
that of the moon in her orbit. The effect of the 
moon's real motion is seen in her rising, southing 
and setting, later and later, day after day or night 
after night. The moon completes her revolution 
round the earth in 27 days, 7 hours, 43 minutes 
and 5 seconds; which is called her periodical revo- 
lution. During this period the earth advances so 
far in her orbit (by which the sun appears to be 
advanced) that it will take the moon more than 
two days longer to overtake the sun again. The 
moon goes from one change, or conjunction with 
the sun, to another, at a mean rate, in 29 days, 12 
hours, 44 minutes and 3 seconds. This period is 
called a mean Lunation. 

2. The moon's orbit is considerably eccentric. 
That point in which she is nearest the earth is call- 
ed her perigee, and in this place she moves with 
the greatest velocity; and the opposite point, where 
she is farthest from the earth, and her motion slow- 
est, is called her apogee. 

3. The moon's apogee and perigee move for- 
ward in the zodiac, making a complete revolution 

4 w ± 



'56 THE VARIOUS PHENOMENA 

In 8 years, 309 days, 8 hours and 20 minutes* 
Thus the moon not only moves with greater and 
less velocity in different parts of her orbit, but with 
the greatest velocity, at one time, where at another 
time her velocity is least, and the contrary. 

4. If the moon's orbit were situated in the plane 
of the ecliptic, it is evident that she would decline 
from the equator north and south once every revo- 
lution (that is about 27 days) as much as the sun 
does once every year. This then accounts, in gen- 
eral, for the moon's running high and low. But 
there is another circumstance to notice respecting 
the declination of the moon. Some years she de- 
clines much farther from the equator than she does 
others. This leads me to observe 

5. That the moon's orbit is inclined to the eclip- 
tic in an angle of about 5 degrees and 9 minutes. 
Now if the moon s ascending node, where her orbit 
crosses the ecliptic from south to north (with the 
forcmentioned inclination) were situated at the 
beginning of the sign Aries, where the eclintic as- 
cends north from the equator in an angle of 23 de- 
grees, 28 minutes nearly; then the obliquity, or 
angle of inclination, of the moon's orbit to the equa- 
tor would be equal to the sum of both those angles, 
viz. 28 degrees and 37 minutes. This then would 
be the maximum of the moon's declination, on the 
supposition that her nodes were thus situated. But 
if the descending n6de were in the beginning of A- 
ries, and the ascending node in the opposite point, 
or Beginning of Libra; then the inclination of the 
moon's orbit to the equator, or maximum of her 
declination north and south from it, would be equal 
only to the difference of those angles, viz. 18 de- 



OF THE VISIBLE HEAVENS. 57 

grees and 19 minutes. But the question arises^ 
Where are the nodes situated? In answer to this, 
I would observe 

6, That the nodes of the mooirs orbit have a 
slow retrograde motion/ and complete a revolution 
round the ecliptic in IS years, 224 days and 5 
hours. This fully explains the mysterious phe- 
nomenon of the moon's running so much higher 
and lower at one time than at another. When the 
nodes are situated according to the former supposi- 
tion (which is the case the present year, 1820) the 
moon will run remarkably high in one part of her 
orbit, and low in the opposite part of it. She will 
decline 28 degrees and 37 minutes north and south 
from the equator, making a variation in declination 
of 57 degrees and 14 minutes; and this variation 
will take place in about fourteen' days ; which is 
half the time of her revolution, for in moving from 
the highest point of her orbit to the lowest point, 
she goes through but one half her orbit. Her dec- 
lination will vary the most rapidly when she cross- 
es the equator; and if she should at the same time 
be about her perigee, the daily variation will be 
increased. This accounts for the vast difference 
in her declination which some have been surprised 
to find lake place in a day or two. 

7. If the plane of the moon's orbit were in coin- 
cidence with the plane of the ecliptic, she would 
eclipse the sun at every change, and be herself 
eclipsed at every full; but as her orbit is so much 
# inclined to the ecliptic, it is manifest that no e- 
clipse can take place except when she is at, or 
near, one of her nodes, at the time of her full ox 
change: because, in any other part of her ort>it f 



£8 THE VARIOUS PHENOMENA 

she will be either too far north or too far south, 
from the ecliptic, either to cast her penumbra on 
the earth at her, change, or to fall herself into the 
earth's shadow at her full. The limits of Solar e- 
clipses are generally stated at seventeen degrees 
from either node on each side; those of Lunar 
eclipses at twelve degrees. But the limits of _e- 
elipses, like every thing else belonging to the 
moon, are subject to some variation. An eclipse 
of the sun is seldom total at any certain place, and 
cannot continue so but a few minutes ; because the 
moon's diameter seen from the earth, when she is 
in perigee, so little exceeds the sun's, even when 
the earth is in aohelion. The limits of Lunar e- 
elipses are smaller and their number fewer than 
those of the sun, because that part of the earth's 
shadow, through which the moon passes in the 
time af a Lunar eclipse, is less than the earth ; but 
there are many more total eclipses of the moon 
than of the sun, because that part of the earth's 
shadow is much larger than the moon. On the 
same account the moon is totally eclipsed for an 
hour and three quarters, as in February, 1812. 

8. The moon's orbit is rendered more eccentric 
than its mean state when the sun is in the same di- 
rection with either her apogee or perigee, and less 
so when the sun is either three or nine signs from 
her apogee. 

9. The moon's orbit is dilated when the earth 
is in her perihelium, or nearest to the sun, which 
is in winter, and contracted in summer, when the 
earth is in her aphelion. 

Thus the eccentricity of the moon's orbit, the 
inclination of the ecliptic to the equator and of the 



OP THE VISIBLE HEAVENS, £9 

moon's orbit to the ecliptic, the motion of the 
apogee and perigee, the retrograde motion of the 
nodes, the variation of flie eccentricity, and the 
dilation and contraction of the orbit, together 
v/ith several other smaller causes which might be 
mentioned, combine to render the moon's motion 
extremely various, in regard to her longitude, lati- 
tude, declination, fulling and changing, southing 
rising and setting. 

10. The rising and setting of the moon, in all 
latitudes from the equator, is also affected by the 
obliquity of the horizon to the equator, and the 
obliquity increasing with the latitude of the place, 
the effect is also increased. The mean daily dif- 
ference of the rising, southing and setting of the 
moon is 50 minutes and 28 seconds of time, but 
the true difference of southing varies from 40 to 68 
minutes; and the rising and setting can differ no 
more or less at the equator, because the horizon 
there, as well as the meridian, is perpendicular to 
the equator ; but in the latitude of New-York, on 
account of the obliquity of the horizon to the equa- 
tor, added to all the other inequalities, the true 
difference of rising and setting varies from 20 to 
80 minutes. 

In many places at a great distance frorn the 
equator (either north or south) the obliquity of the 
horizon is so great that its inclination to the equa- 
tor is even less than that of the moon's orbit. At 
I those places the moon may sometimes be observed 
'to rise or set earlier and earlier for a few successive 
nights or days, instead of later and later as with 
us. This phenomenon may sometimes be seen at 
Greenland, Davis's Straits., Hudson's Straits and 



60 THE VARIOUS PHENOMENA., cVC. 

the northern parts of Hudson's Bay, Slave Lake, 
Cook's Inlet, and "all places on the globe at equal 
or greater distance from the equator. 

We see then that the moon's motions and phe- 
nomena, although various as can well be conceiv- 
ed, are all fixed and certain; the effect of certain 
determinate motions and laws, without the knowl- 
edge of which no calculations whatever on the 
subject could possibly be made. 



* LECTURE THIRD. 

An explanation of the Method by which the Mag- 
nitudes and Distances of the Sun and Planets 
have been determined. 

LOW and gradual was the progress of Astron- 
^J omy in ancient times on account of their igno- 
rance of the mathematics, and their want of math- 
ematical instruments and tables. One improve- 
ment and one discovery must first be attained in 
order to prepare the way for another. It was long- 
before any rational hypothesis was suggested — 
Various were the opinions of philosophers, as is 
alwavs the case with mankind while involved in 
the darkness of errour, prejudice and superstition ; 
and while the subjects which agitate them remain 
mere matters of uncertainty and conjecture. Their 
oninions differed because they were nothing more 
tiian opinions. And when at length the true hy- 
pothesis was suggested, and adopted, a long course 
of observations was necessary in order to ascertain, 
with any decree of precision the motions of the 
planets, the inclinations of their orbits, the degree 
of their eccentricities, the situation of their nodes 
and aphclia; and especially to determine with 
any accuracy either the mean or the true motions 
of the moon. And after all, their opinions were 
various respecting the real distances and magni- 
tudes of the sun, planets and stars ; because these 
were subjects concerning; which they had as yet no 

F 



62 THE MAGNITUDES AND DISTANCES 

knowledge. The attainment of this knowledge^ 
though not in the least degree necessary in order to 
calculate with the utmost precision all the phenoiu- 
ena of the visible heavens,* was nevertheless a 
very desirable object with them. It was not prac- 
ticable, however, until calculations could be made 
with considerable accuracv. To shew that it is 
ultimately practicable is my object on the present 
occasion. 

1 . I shall in the first place show that the com- 
parative distances of the planets were known before 
their real distances were, or could be, discovered. 

"2. I shall show in the second place how the 
magnitude of the earth has been determined. 

3. How the distance and magnitude of the 
moon have been found shall be shown in the third 
place. 

4. Fourthly, I shall show the method by which 
the distance of the earth from the sun has been as- 
certained, together with the magnitude of the sun. • 

5. In the fifth place I propose to show how the 
distances of all the planets from the sun, and their 
dimensions have been discovered. 

6. Lastly, I shall make some observations res- 
pecting the magnitude and distance of the fixed 
stars. 

I. The proportion which the distances of the 

several planets from the sun bear to each other was 
_ 

# I mean here to except Solar and Lunar Eclip- 
ses, and all other phenomena of the moon. But 
the moon's true distance and magnitude ivere 
knoicn before, and were discovered in the manner 
hereafter explained. 



OP THE SUN AND PLANETS. 63 Jf 

known before their true distances were. Kepler 
discovered that the squares of their periodical times 
were to each other as the cubes of their distances. ; 
This law he might have discovered by the satellites 
of Jupiter or Saturn, the periods and distances of 
which could be determined by observation; I mean 
their distances, reckoned in semidiameters of their 
primary. The squares of their periods are in ex- 
act proportion to the cubes of their distances reck- 
oned thus. Their distances bear the same pro- gj 
portion to each other reckoned in one measure, that m 
they do reckoned in any other measure; so that if 
the distance of one of them were known in miles, 
the distances of the others in miles also might be ~ 
found by the rule above stated. I wish to have it 
understood that this rule holds good throughout any 
certain set of planets. The square of the period 
and the cube of the distance of one secondary, are 
jn the same proportion to each other, that those are 
of any other secondary revolving around the same 
primary, and not those of a secondary belonging to 
a different primary. A body of a different weight 
at the centre of the orbit will alter the proportion 
between the distance and velocity of the revolving 
body. If the sun were heavier than he is, the plan- 
ets "would need a swifter motion to balance his 
greater attraction. But with respect to the revolu- 
tions and distances of any distinct set of planets, 
either primary or secondary, the above proportion, 
or law, hoWgood. This law is observable among 
the satellites of Jupiter, Saturn and Herschel, and 
was demonstrated by Sir Isaac Newton. Now the 
periodical times of the planets being known by ob- 
servation, their comparative distances may easily 



64 THE MAGNITUDES AND DISTANCES 

be computed by the foregoing rule. Any bomber 
may be assumed as the distance of a certain plan- 
et, and the distances of the others computed by it, 
according to the above rule, will be proportional. 
Thus, assuming for the earth's mean distance from 
the sun 100,000, we find the true relative mean dis- 
tances of the primitive planets to be as follows, viz. 
Mercury 3 8,71 0, Venus 7-2,333, the Earth 100,000, 
Mars 152,411, Jupiter 519,958, Saturn 953^133, 
and Herschel 1, 904,561. 

The distance of a planet in any part of its orbit, 
in proportion to its mean distance, was also known 
before any thing radical was known respecting 
their distances. Thus if we assume 100,000 as 
the earth's mean distance, then her distance in her 
aphelion will be 101,692, and in her perihelium 
98,308. The earth's relative distance, in any part 
of her orbit, was discovered by the apparent diam- 
eter of the sun, which varies from 31 minutes and 
34 seconds to 32 minutes and 38 seconds. The 
earth's daily motion in her orbit, which is the same 
as the sun's apparent motion in the ecliptic, was 
found to vary from 57 minutes and 12 seconds to 
6l minutes and 10 seconds. From these data it 
appeared by calculation that an imaginary line ex- 
tending from the earth to the sun and carried round 
with the earth, would pass over, or describe, equal 
areas in equal times. This, by means of a variety 
of nice observations and calculations, was found to 
be an universal rule or law. This law was also 
discovered by Kepler and demonstrated by Newton. 
The mean motions of the planets were directly de- 
termined from the times of their revolutions : but 
to ascertain their true motions, in tli2 various pails 



OF THE StfS ANB PLANETS. 



63 



Of their orbits, required a series of observations and 
some nice calculations -which I have not time to 
describe. I wish to convince you however of the 
tact that their true motions were determined, and 
I think the following observation sutticient tor tins 
purpose. It is certainly a fact that they coura pre- 
cisely calculate the phenomena of the planets, their 
conjunctions, oppositions and other aspects, toe 
times and even all the phenomena of transits ; but 
how could this be done without a knowledge of the 
true motions of the planets ? From a knowjecge 
then of the true heliocentric motions of the planets 
in every part of their orbits, and a knowledge o. the 
law inst mentioned, they could easily determine- 
the relative distances of the planets irom the sun m 
all parts of their orbits. 

II I was next to show how the magnitude ot 
the earth has been determined. This has been 
done by measuring a degree on the arc ot a great 
circle, either the equator or some mencuan, the om- 
its of which had been determined by the stars. A 
degree was thus found to measure 69-t ^nghsli 
miles. This multiplied by 3 60, the number ot de- 
grees in a circle, gives 25,320 miles for the whole 
circumference of the earth. Then from the pro- 
portion between the circumference and diameter ot 
a circle, we find the diameter of the earth to m 
7064 miles, and its semkhameter 3932 nurs. _ 

III In what manner the distance and magnitude 
of the moon have been discovered was to be saovn 

hi the third place. # 

i If the real and apparent size of a celestial bo- 
dvbe riven, its true distance may te discovered 
iy the following method, viz. as the tangent of hail 
J ■ F 2 



60 THE MAGNITUDES AND DIST VNCES 

the angle under which it appears,- or the tangent of 
its apparent semidiameter, is to radius ; so^ is its 
real semidiameter to its true distance. Now the 
semidiameter of the earth is given above, and its 
apparent semidiameter seen from the moon (which 
is called the moon's horizontal parallax) may be 
determined by . the difference between the time 
when she appears to rise or set, and the time when 
she would appear to set or rise if she had no such 
parallax^ This then will enable us to determine 
the earth's distance from the moon, which is the 
same as her distance from the earth. In this man- 
ner the moon's horizontal parallax has been found 
to be, when she is in apogee 54 minutes and 2 
seconds, and when in perigee 6l minutes and 33 
seconds, making her distance from the earth in the 
former case 253,325 miles, and in the latter 222 
390 miles; and therefore her mean distance is 
237,857.5 miles. 

2. If the true distance and apparent semidiame- 
ter of a planet be given, the real semidiameter may 
be found in the following manner. As radius is to 
the tangent of the apparent semidiameter, so is the 
distance to the true semidiameter. The moon's 
apparent semidiameter when in apogee is found by 
observation to be 14 minutes and 45 seconds, and 
when in perigee 16 minutes and 48 seconds. In 
either case the true semidiameter turns out to be 
1087 miles,- so that the moon's diameter is 2174 
miles. The content of the moon then, in cubic 
miles, is to that of the earth as 1 is to 49, and the 

area of her convex surface, as 100 is to 1342. 

This last is also the proportion which the light she 
affords the earth bears to what she receives from 
the earth. 






OF 'THE SUN AND PLANETS. 67 

IV. The fourth' proposition was to show the 
possibility of determining the earth's 'distancerfrom 
the sun, together with the sun's magnitude. 

Were the sun's horizontal parallax known, his 
distance from the earth might be found in the same 
manner in which the moon's distance was ; but the 
sun's horizontal parallax is so very small that every 
attempt to discover it in the way in which the 
moon's was discovered, has proved unsuccessful ; 
some other method therefore must be resorted to in 
order to obtain his parallax. 

When either of the inferiour planets makes a 
transit across the centre of the sun's disk seen from 
the earth's centre, the centre of its penumbra pass- 
es over the centre of the earth's disk seen from the 
sun's centre, I have premised that all the phenom- 
ena of the visible heavens may be calculated to as 
good advantage only by a knowledge of the com- 
parative distances of the planets, which was previ- 
ously known, as by a knowledge of their true dis- 
tances. That line also, across the centre of the 
earth's disk^ which an inferiour planet, seen from 
the sun, would appear to describe in a central tran- 
sit, may be particularly determined, together with 
the latitude and longitude of those places through 
which it would pass. The apparent motion of an 
inferiour planet is always retrograde at the time of 
an inferiour conjunction ; so that the motion of the 
planet on the sun's disk, and the motion of the 
penumbra on the earth, are always from east to 
west. An observer stationed near that point of the 
earth's surface which will be in the eastern boun- 
dary of her disk, and at one extremity of ihe fore- 
mentioned line, when the penumbra's centre arrives 



68 THE MAGNITUDES AND DISTANCES 

there, wjB perceive all the phenomena of the transit 
a little earlier than one stationed in that place 
which will be in the western boundary of the disk 
at the other extremity of the line. This difference 
of time, whatever it might be found by observation^ 
is the time in which the planet wouM traverse the 
earth's disk seen from the sun ; and consequently 
the difference between the heliocentric motion of 
that planet and of the earth, for this interval of 
time, will be equal to the apparent diameter of the 
earth seen from the sun, or double the sun's hori- 
zontal parallax. 

A transit of Venus is more convenient than one 
of Mercury, for this purpose, on account of her 
slower motion. The interval of time abovemen- 
tioned will be of longer duration, and therefore the 
parallax determined with the greater precision. — 
For if the interval, as near as can be observed^ 
should vary one second of time from the truth (as 
might reasonably be expected) when the whole in- 
terval is only one hundred seconds ; then the par- 
allax thus obtained might vary from the truth by 
the one hundredth part of itself ; but the variation 
of one second in an interval of five hundred sec- 
onds, will occasion an error in the parallax of only 
the one five hundredth part of what it really is, and 
the distance to the sun obtained by it would vary 
from the truth at the rate of only one mile in five 
hundred miles. Thus a transit of Venus is more 
convenient for the purpose than one of Mercury. 

When the centre of the penumbra is at any point 

on the earth's surface, the centres of the sun and 

the planet are in contact seen from that point ; 

i^i^h circumstance cannot be determined so- pre* 



OF THE SUN AND PLANETS, 

cisely as that of the first impression made b\ 
planet on the sun's disk, called the external conts 
or the beginning of ingress ; or as that oi its having 
wholly entered upon the disk, called the internal 
contact, or total ingress. It would be better there- 
fore to station the observers in such places that one 
may observe the two contacts at the ingress from 
the eastern, and the other from the western boun- 
dary of the earth's disk seen from the sun at that 
time, and so that a straight line from one to the 
other shall pass over the centre of the disk. 1 he 
observation of either the external or internal con- 
tact alone from both places would be sufficient* 
provided it should be exactly determined ; but it 
both be observed it will amount to two experiments, 
and the mean result of khe two may probably be 
more accurate than either alone ; besides it is safer, 
for one contact might be visible at both places, and 
the other not, being obscured by flying clouds. It 
is highly proper also, in order to avoid disappoint- 
ments as much as is possible and to heighten the 
probability of success, that the contacts at the egress 
should be observed by persons stationed in the same 
relative positions as were before described with re- 
spect to the ingress ; for otherwise the accomplish- 
ment of the object in view would fail, if at either of 
the places the observations should be prevented by 

clouds. 

►The observers should set out for the places oi 
their destination in due season, making large allow- 
ance for adverse winds and other casualties ; and 
should arrive, with their assistants and their ap- 
paratus, some weeks previous to the transit, in or- 
der to have their clocks set and regulated with tlie 



<fO THE MAGNITUDES AND DISTANCES 

utmost care and precision, and all other things in 
readiness. 

If local circumstances render it inconvenient, it. 
is not necessary that an observer should be pre- 
cisely at the spot calculated upon. Fifty or an 
hundred, or even an hundred and fifty miles will 
not either essentially or perceptibly affect the result 
of the observation, provided that his situation be in 
the line which has been described ; provided also 
that the one near the eastern boundary of the earth's 
disk be not so far east that the sun will set to him 
before the contacts take place, and the one near 
the western boundary, not so far west that the con- 
tacts take place before the sun rises. It will be 
his business however to determine precisely the 
longitude\ofthe place where he makes his stand. 
This may be done either before the transit or after 
it, but it must of necessity be done in order to know 
the true difference of time between the meridians, 
without which the interval of absolute time which 
elapses between the appearance of a certain contact 
at one station and the appearance of the same con- 
tact at the other station, cannot be determined ; 
which is the all-important object in this business. 

I would observe further that whereas a central 
transit very seldom occurs, and perhaps seldom one 
so nearly central as that the eentre of the penumbra 
comes at all upon the earth's disk, yet that a line a- 
cross the centre of the disk, as before described, m 
a direction parallel with the line or path of the pe- 
numbra's centre, will in every respect answer the 
proposed purpose. 

If all these things be punctually attended to in 
l&e time of a transit of Venus, the horizontal par- 



OF THE SUN AND PLANETS. fl 

allax of the sun, and consequently his distance, will 
be obtained to within a five hundredth part of what 
it really is : unless that Great and Good Being, who 
is superlatively so, see it best to prevent. 

Suppose now that at the transit of Venus on the 
6th of June, 1761, the interval of time which we 
have before so frequently alluded to was found to 
be 10 minutes and 45 seconds. The mean motion 
of Venus in her orbit for this interval, as you may 
easily calculate from the time of her revolution, is 
43 seconds and 3 thirds, but as she was within 
about 53 degrees of her aphelion at that time, her 
true motion for the above interval was only 42 se- 
conds and 41 thirds. The earth's mean motion 
for the same time is 26 seconds and 29 thiids, but 
being within 24 degrees of her aphelion at that 
time, her true motion w^as only 25 seconds and 41 
thirds. The difference then between the true he- 
liocentric motion of the earth and Venus for this 
interval was IT seconds ; the half of which, 8 se- 
conds and 30 thirds, was the sun's horizontal par- 
allax at that time, being less than its mean quanti- 
ty, because the earth was so near her aphelion.— 
JXow as the tangent of this parallax is to radius, so 
is the semidiarneter of the earth (3982 miles) to its 
distance from the sun at that time, The result is 
96,628,888 miles. It was well known before that 
the earth's distance from the sun in that point of 
her orbit was to her mean distance as 101,550 is to 
100,000. Hence the mean distance appears to be 
95,1 54,000 miles. This was very nearly the result _ 
of the observations made at that time. Mr. Short, 
who spared no pains to ascertain the mean result 
of all the observations which were made, I think 



?'2 THE MAGNITUDES AND DISTANCES 

stated it at 95.173,127 miles. There was another 
transit on the 3d of June, 1769, when the result of 
the observations w r as the same as before. The 
next will be on the 8th of December, 1874, 

Now the sun's distance having been obtained, 
and his apparent semidiameter at any time being 
well known, his magnitude may be determined in 
the following manner. As radius is to the tangent 
of the sun's apparent semidiamter so is his distance 
to his true semidiameter. Therefore either take 
his mean distance, given above, and his mean ap- 
parent semidiameter, 1 6 minutes and 2 seconds $ or 
his distance on the day of the transit, given also 
above, and his apparent semidiameter on that day, 
which was 15 minutes and 47 seconds. The result 
in either case makes the sun's true semidiameter 
443.731 miles, so that his diameter is 887,462 
miles. The sun then is as large as 1,383,748 of the 
earth, or as 68,025,625 of the moon. 

V. I was to show in the fifth place how the dis- 
tances of all the planets from the sun,, and their 
magnitudes have been found. 

I. The distances of the planets may be obtain- 
ed from their comparative distances, mentioned in 
the former part of this lecture, by the rule of pro- 
portion. As 100,000. the earth's proportional dis- 
tance there given, Is to her true distance in males ; 
so are the proportional distances of the others to 
their real distances in miles. Or you may say, As 
the scjuare of the earth's periodical revolution, is 
to the cube of her mean distance from the sun; so 
is the square oi any other planet's period, to the 
cube of its mean distance. Thus the true mean 
distances of the primitive planets will be found ts 



> 



OF THE SUN AND PLANETS. 



ts 



fee as follows. The mean distance of Mercury m 
36,841,949 miles; that of Venus, 68,841,587; that 
of the earth (as mentioned before) 95,173,127; that 
of Mars, 145,054,515; that of Jupiter, 494,860, 
227; that of Saturn, 907,125,000; that of Hers- 
diel, 1,812,631,799 miles. 

2. I come now to show how the magnitudes of 
the other primary planets were determined. 

Their apparent diameters, or semidiameters, and 
their respective distances from the earth, are all 
the necessary data; these being obtained, work as 
before in finding the sun's magnitude. As radius 
is to the tangent of the planet's apparent semidiam- 
c-ter, so is its true distance from the earth to its real 
semidiameter. The apparent diameter must be ta- 
ken by observation, and the true distance determin- 
ed by calculation. As the distances of all the other 
planets from the earth, and consequently their ap- 
parent magnitudes, are subject to great and contin- 
ual variation, it will be necessary to determine both 
these articles for the same period of time. The 
apparent diameter may be taken when there is a 
convenient opportunity, and afterwards the distance 
from the earth calculated for the same time. Find 
the distance of the earth, and of the planet whose 
magnitude is sought, from the sun, for the given 
time; together with the difference of their helio- 
centric longitude; then, by plane trigonometry, 
the distance of that planet from the earth may be 
found. But there are times peculiarly favourable 
for this business, when it may be done with greater 
accuracy and less trouble. The time of the oppo- 
sition of a superiour planet is the best to take its 
Apparent diameter 5 because, being nearer the earths 

G 



74 THE MAGNITUDES AND DISTANCES 

it appears larger, and we are not liable on that ac- 
count to an error so great in proportion. It is the 
most convenient time also to determine the planet'3 
distance from the earth, which at such times is al- 
ways equal to the difference between the earth's 
distance from the sun and the planet's distance from 
it. With regard to an inferiour planet, the time of 
a transit is perhaps the most favourable of any to 
take its apparent diameter, and to determine its dis- 
tance from the earth also, which at those times is 
likewise equal to the difference between its distance 
from the sun and the earth's distance. 

Thus we see that the distance of any planet from 
the earth, as well as from the sun, at any time may 
be found ; but with less inconvenience at particu- 
lar times when its apparent diameter may be taken 
by observation to the "best advantage ; which two 
things are necessary in order to determine its real 
magnitude. The distance of Mars from the earth 
is more various than that of any other planet.— 
When in conjunction with the sun, and in aphelion, 
his distance from the earth is no less than 254,660 ? 
000 miles ; but when in opposition, and in perihe- 
lium, it is no more than 35,400,000 miles. The 
angle under which his semidiameter is seen in the 
latter case is 1 5 seconds of a degree. Taking the 
last mentioned distance, with the apparent semidi- 
ameter at the same time, 15 seconds, we shall find 
hy trigonometry, his real semidiameter to be 2575 
miles, or his diameter 5150. In this manner the 
diameters of the planets were determined. Mercu- 
ry is 3,222 miles in diameter ; Venus, 7>690 $ the 
•arth, 7,964 j Mars, 5,150; Jupiter, 94.100; Sat-- 
mm, 78,990 ; and Herschel, 35,226, 



dF- THE SUN AND PLANETS- 7'5 

VI. The distances of the fixed stars were to be 
spoken of in the last place. 

It is lawful to speak of things which are beyond 
•our calculation or comprehension. We may speak 
of eternity and immensity, either of which is beyond 
the comprehension of Gabriel. The distance of 
the fixed stars we can never determine, yet it is not 
a subject which we know nothing about. 

The greatest difference between the situation of a 
star seen from the earth, and its situation seen from 
the sun, may be called the annual parallax of that 
•star. If this difference could be found, the distance 
of the star might be determined ; for as the tangent 
of this parallax is to radius, so is the semidiameter 
of the earth's orbit to the distance of the star. But 
every attempt to discover the annual parallax of 
any, even the brightest, of the stars, which are 
therefore supposed to be nearest, has proved unsuc- 
cessful. A parallax cannot but exist, but the small- 
ness of the angle renders it imperceptible. Astron- 
omers have thought that if it amounted to one se- 
cond of a degree, that is if the whole diameter of 
the earth's orbit appeared from the stars under an 
angle of two seconds, it would have been discovered; 
but to keep altogether within bounds I will suppose 
that the parallax might be sixty times as great in 
order to have been observed. I will suppose the 
semidiameter of the earth's orbit seen from the near- 
est star is less than one minute of a degree, because 
otherwise the parallax would have been perceived, 
Let us look at the distance on this supposition. As 
the tangent of 1 minute is to radius, so is §5,1,7 > 3j 
327 miles, or the semidiameter of the earth's orbit, 
to 327.200,000,000 miles. To fly this distant 



J 6 THE MAGNITUDES AND DISTANCED 

would take a body, moving at the rate of 480 rniles^ 
an hour, 97,8 10 years. The nearest of the iixed 
stars is at least thus far distant from our system ; 
how much farther than this, it is impossible for us 
to determine. We have reason to believe that this 
bears a very small proportion to the distance of 
those which shine so faintly in the cerulean fields, 
and that it dwindles into insignificancy in compari- 
son with the distance of those millions, those innu- 
merable multitudes, which the unassisted eye never' 
can discover. The very appropriate exclamations 
of a celebrated poet, who flourished about one hun- 
dred years ago, force themselves upon my mind. 

44 What involution ! what extent ! what swarms 
Of worlds that laugh at earth ! immensely great ; 
Immensely distant from each other's spheres ! 
What then the wondrous space through which they roll? 
At once it quite ingulphs all human thought ! 
^is comprehension's abso'nt? defeat !" 

From the vast distance of the fixed stars, we con- 
dude without hesitation and with absolute certainty 
that they are not opaque bodies, shining by the re- 
flection of the solar rays, but that they are lucid 
bodies, emitting their own lustre. Such is their 
distance that our sun, great as it is, appears like a 
star and can no more supply them with light than 
they can furnish him. Such is their magnitude 
that they must be ranked with him in the order of 
creation, or they could never be discovered from 
such a distance. From these certain truth's and 
from analogy, it is rational to infer that they are 
suns, surrounded each by a set of planets and se- 
condary planets which from their distance we can 
never actually discover. All these primary and 
secondary planets are doubtless the abodes of ra- 
tional beings > as well as those of our own system 



OF THE SUN AND PLANETS. pf 

Having; travelled thus far in the unbounded re- 
-gions of immensity, let us for a moment survey the 
galaxy. We find it to consist of systems in clusters ; 
clusters involved and buried in clusters, in such pro- 
fusion that a thousand systems would not be missed 
anv more than a twig taken from a forest ! And af- 
ter all we have no adequate conceptions oi the ex- 
tent or the magnificence of the universe. Could 
' we actually take our departure from this cluster of 
creation, and pass through that profundity of unoc- 
cupied space which surrounds it, and visit the most 
distant nebulae which the telescope can discover; 
what should we still know of the Empire of the Inn- 
nite and Eternal SOVEREIGN ! How vast are 
his dominions ! How language fails in the descrip- 
tion ! Some borrowed expressions: though very in- 
.tdecjuate, may better answer my purpose than any 
which I might frame. 

il Is do! this home creation, Id the msp 
Of universal nature, as a speck ;' 



May ve not figiuje it an isle, almost 

Top small \ov notice ia the vast of being? 

Sever'd by mighty seas of unbuilt space 
From other realms; from ais.>le continents, ,>: 



. Where? 

Where end? this mighty building? Where begin 
The suburbs of creation ? IV here the wall 
"Whose battlements look o'er into the vale 
Of nonexistence, nothing's strange abode f 
Sevat^hat point of space Jehovah dropo'4 

G 2 



7$ THE MAGNITUDES AND DISTANCES &C. 

His slackenM line and laid his balance by? 
Weigh'd worlds and measured infinite no more? 
Where rears his terminating pillar high 
Its extramundane head, and says to gods, 
In characters illustrious as the sun, 

I stand the Plan 's proud period: I pronounce 
The Work accomplished; the Creation ch^d?? 



j~* 



LECTURE FOURTH 

The Causes of the Ebbing and Flowing of the Sea 
explained; together ivith the Manner in which 
the Motion of Light was discovered; as also, 
the Consistency of the Motion of a Planet or 
Comet in an eccentric or elliptical Orbit. 

N the rapid progress which we have made in the 
preceding Lectures, several subjects worthy of 
attention have been passed by unnoticed. My de- 
sign at present is to bring them under considera- 
tion ; and I hope to bestow on them that attention 
which their importance may demand. I propose 

First, to illustrate the causes of the ebbing and 
flowing of the sea; 

In the second place, to explain the method by 
which the motion of Light has been discovered, 
and its velocity determined; 

Thirdly, to" show the consistency of the motion 
of a planet or comet in an eccentric or elliptical or- 
bit. 
I. An illustration of the causes of the ebbing and 

flowing of the sea, is the first proposition. 

That this effect is produced by the influence of 
the moon is a rational conclusion, from the circum- 
stance of its having, throughout all ages, precisely 
kept pace with the apparent daily revolution of that 

luminary. 

But the grand queries, I apprehend, are, How is 
such an effect produced ? and, Why are there two 
ebbs and two flows m one. apparent revolution, 



BO TBE EBBING AND FLOWING OF THE SEA* 

whereas the earth has but one moon ? The usual 
reply to these queries, and which is all I recollect 
to have read on the subject, is far from giving en- 
tire satisfaction. When we say, "the waters on 
the side of the eaith next the moon are elevated bv 
the moon's more powerful attraction, and those on 
the opposite side are elevated by her less powerful 
attraction/' 7 we leave the subject in the same obscu- 
rity m which we found it. A less degree of attrac- 
tion cannot amount to a repulsion. In the sequel 
it w;H -pear that such an effect must be produced • 
and that there must be two ebbs and flows in one 
Lunar day, will appear with as much certainty as 
that there must be one. By a Lunar day, I mean 
the time from one southing of the moon to another 
which is at a mean rate, 24 hours.,, 50 Minutes 2$ 
seconds. I will, - ; 

In the first place, give a theory of the tides 
Secondly, apply ft to the earth, and 
Thirdly, answer objections ikU may arise. 
I. A Theory of the Tides. 
1 have observed, perhaps once and again* that 
the time oi a planet's revolution in its orbit, or its 
velocity, must bear a certain proportion to its dis- 
tance from the sun : in order that the centrifugal or 
projectile force, may exactly balance the sun's at> 
Traction^ which is also called the centripetal force. 
This proportion has been found to be such that the 
square of the time of a planet's revolution round 
me sun, must increase or decrease with the cube of 
its distance from it. Thus, by calculation it will 
be found, that if a planet were situated twice as far 
from the sun as the earth is, the time of its revolu- 
tion must be two years and 303 days; if three times 



THE EBBING AND FLOWING OF THE SEA. 81 

the earth's distance, its period must be 5 years and 
72 da}s; and if it were situated four times as far 
from the sun as the earth is, the time of its revolu- 
tion must be just 8 years. Any certain velocity, 
then, or any certain periodical revolution, evident- 
ly requires a certain distance ; and the distance of 
•each planet is such as its velocity requires, or its 
velocity such as its distance requires, 

If it were possible for a planet revolving in a per- 
feet circle to be removed instantaneously to a great- 
er distance from the sun, without affecting its velo- 
city, it would immediately have a tendency^ to 
recede farther still from the sun $ for its velocity, 
being too great to balance- the sun ? s attraction, 
would carry it forward in a line of less curvature 
than that of a circle whose centre should be at the 
sun. Its orbit would therefore become eccentric ; 
the place where the change of distance took place 
would be its perihelium ; its mean distance would 
be greater than that to which it was removed, and 
Its mean velocity less than before. The reverse of 
all this would take place on the supposition of its 
being removed nearer the sun without any altera- 
tion In its velocity. On account of the sun's too 
powerful attraction, it would fall within the com- 
pass of a circle ; its orbit would become eccentric ; 
the point where the change of distance took, place 
would be its aphelion ; its mean distance would be 
less, and its mean velocity greater than at that point, 
or than it was before. What I wish you particu- 
larly to notice here is, the tendency of the planet, 
on the former supposition, to recede farther from 
the sun on account of his weaker attraction, while 
the planet's velocity suffers no diminution 5 and its 



£2 THE EBBING AND FLOWING OF TH#SEA„ 

tendency, on the latter supposition, to approach 
nearer to the sun, on account of his greater attrac- 
tion, the planet's velocity not being increased. 
^ Now when we say the distance of a planet from 
- tne sun is such as its velocity requires, how do we 
wish to be understood ? Certainly thus, that the 
centre of the planet is at such a distance from the 
sun's centre as its velocity or revolution requires. — 
Every part of a planet goes round the sun in the . 
same time, but every part is not equally distant % 
irom ihe smrs centre. The side of a planet, there- 
fore, nearest the sun has not sufficient velocity to 
balance the sun's attraction, which is more power- 
ful there than at the centre of the planet. On the 
contrary, that part of a planet farthest from the sun, 
has too great velocity to balance the attraction of 
the sun, it being weaker there than at the planet's 
centre. 

Let us now look at the effect of this dispropor- 
tion between the distance of some parts of a planet's 
body, and their velocity. 

1. The tendency of the nearest part of a planet 
to fall towards the sun, and of the farthest part to 
fly oil from it, balance each other, so that the plan- 
et is retained in its orbit notwithstanding. 

2, Suppose there were a planet, whose figure 
was a perfect sphere, consisting entirely of solid 
substances, that is, substances not fluid, which 
should revolve around the sun, and on its own axis, 
in trie same period of time ; thus Seeping the same 
point at all times towards the sun. All bodies on 
its surface towards the sun would fcave less weighs 
on account of their tendency to fall to the sun ; and 
those on the opposite side would be lighter, in cor 



"THE EBBiNO AND FLOWING OF THET SEA. 

sequence of their tendency to fly off from the sun. 
The disproportion must be extremely great in or- 
der entirely to balance their gravity, or to overbal- 
ance it. 

3. If this same supposed planet .should revolve 
on its axis with greater velocity, the effect would 
be the same, except that those parts where the 
weight of bodies w r ould be diminished, would be 
on different sides of the planet by turns, being al- 
ways towards and from the sun. 

4. Let us look at the effect of this same dispro- 
portion on a supposed planet entirely aqueous ofe 
fluid, revolving round the sun with the same point 
at all times towards him. The tendency of one 
side to fail towards the sun, and of the other to re- 
cede from it ? would reduce its figure to an oblong" 
spheroid, with its longest diameter directly tow- 
ards and from the sun. 

5 . Let this aqueous planet be supposed to revolve 
with greater velocity on an axis perpendicular to 
the plane of its orbit, or not greatly inclined to 
It. This rotation would throw it into the form of 
an oblate spheroid. Yet its equatorial diameter 
would be longer in a certain direction than in any 
other, not perhaps in a direction to and from the 
sun. The revolution on its axis could not destroy 
the effect before spoken of, but the elevations of the 
fluid might be driven forward by it a certain dis- 
tance, according to the velocity of its motion • in 
the same manner that a small swell of water on the 
under side of a grind-stone, when it is in motion, 
will be carried some small distance past the very 
lowest point of the surface of the stone, by its mo- 
£b». A query must arise. Why is there not $ 



34 THE EBBING AND FLOWING OF THE SEA. 

small swell of water also on the upper side of the 
stone ? Answer. There would be, if the stone 
were supported from failing to the earth by a cen- 
trifugal force. 

6. Suppose a terraqueous planet, like the earth, 
should keep the same points of its surface continu- 
ally to and from the sun, throughout its annual rev- 
olution. The waters would be elevated on the sides 
towards the sun and opposite to him ; but there 
would be no ebbing and lowing, because the two 
opposite protuberances would be stationary on the 
same points of the planet forever. 

7. Let this terraqueous planet be caused to re- 
volve, from west to east, on an axis not extremely 
inclined to the plane of its orbit. Immediately an 
ebbing and flowing of the waters will be perceived 
Tilong the coasts of continents and islands; because 
different parts of the planets surface will alternate- 
ly be turned to those points where the waters are 
elevated, and also to those where they are de- 
pressed. These elevations or flows of the water 
will be carried forwards a certain distance, from the 
direction to and from the sun, by the revolution of 
the planet on its axis : and probably this distance 
will be much greater on a terraqueous than on an 
aqueous planet: but the flow and the ebb will both 
t>e perceived twice in every revolution, or, more 
precisely, twice in that period of time in which any 
.point of its surface will be turned from the direction 
of the sun to the same direction again ; which is al- 
ways a little different from the time of a revolution 
on its axis, on account of its motion in its orbit in 
%he mean time. 

<&, We will now suppose this planet t© have a 






THE EBBING AND FLOWING OF THE SEA. 85 

secondary planet, or moon, revolving around it 
from west to east; performing several revolutions 
during one revolution of the primary round the 
sun. This secondary planet must also produce aa 
ebb and flow in the waters of the primary, twice in 
the time in which the primary would turn a certain 
side from the secondary to it again ; which would 
be a longer time than that in which it would turn 
from the 5 sun to the sun again $ because the secon- 
dary would make a greater advance in its orbit 
round the primary in that time than the primary 
would in its orbit 'round the sun. When the sun 
and secondary planet are either in conjunction or 
opposition seen from the primary, their effect on 
tire waters will coincide ; the flow will be higher 
and the ebb will be lower than would be caused by 
die single influence of either. On the contiary, 
when their apparent situation is ninety degrees a- 
sunder, the influence of one will destroy or dimin- 
ish the effect of the other. 

II. I shall now briefly apply the foregoing theo- 
ry to thp earth. 

The earth revolves on her axis in such a period 
of time that any meridian is turned from the sun to 
the sun a^ain in 24 hours ; consequently there will 
be two flows and two ebbs of the sea in every such 
period, depending on the sun's influence. The 
earth turns any meridian from the moon to the 
moon again in 24 hours, 50 minutes and 28 seconds, 
at a mean rate, which period I have called a mean 
Lunar day ; therefore two ebbs and flows of the 
sea, produced by the moon, will be perceived in 
every such period. 

The Solar influence on the waters produces but 

H 



. , 



86 THE EBBING AND PLOWING OP THE SEA. 

i little effect. Some have stated it at one fifth part 
of the effect produced by the influence of the moon ; 
hut I think this estimate too large. It is however 
perceptible in causing the Lunar flows and ebbs to 
run higher and lower about the full and change of 
the moon, when the influence of the sun and moon 
are united, and in the contrary effect at the quarters 
of the moon. ' 

The attraction of the sun upon the earth is prob- 
ably as great as that of the moon, and perhaps 
greater, but its enect on the waters cannot be in 
proportion to the strength of attraction. Attrac- 
tion may be ever so p< :. werful, yet, if all parts of the 
globe are ■ equally attracted, there can be no such 
effect produced. Suppose the mooa's centre were 
three semidiameters of the earth from the earth's 
centre, which would be one diameter of the earth 
from its surface. One side of the earth, en this 
supposition, would be twice as far from the moon 
as the other : and if the power of attraction decreas- 
ed with the increase of the distance, the side of the 
earth next the moon would have double the attrac- 
tion that the other side would. , The diameter of 
the earth would bear so great a proportion to the 
distance .of the moon, in this case, thai it would oc- 
casion this difference of attraction. But suppose 
the moon to be sixty semidiameters of the earth 
from its centre ■; then the proportion which the 
earth's diameter would bear to the moon's distance 
would be much less, and the difference of the moon's 
attraction on the different sides of the earth conse- 
quently proportionally less. The sun's distance 
from the earth is 396 times as great as that of the 
moon, and on account of its vast distance it cannot 



THE EBKING AND PLOWING OP THE SEA. 5? 

attract side of the earth much more powerfully 
ther, because one si k is but a " -: ' small 

- 

portion ne rei ::■ hi am than tb* Jther. 
The] .-rorb. vnceoiarr: ; _ ;. does not 

. the increase of the distance^ 
ith the increase o he square fthedi- tanc -. 
If then the rreofthi mc were three seroidi- 
an: f the earth frcm the earth's centre, as we 

jus pposedj die degree of the mc a's attrac- 

tion on the ne st side of the rarth. on her centre 
and on hei rthersi z in I ic proporti 

: L mc 4. Bv this we see that the tide on 

WW 

■ ■ .. . ek 11 be pies Iser than . laf on 

thee ate side jftheeartk The proportion oa 
the | at sup] :'::". for the 

dii :e be q 1 . and ". andthe in*€ a 

betwe-.. > and 4 is .". it a greater instance . 

■ moon leave a less difference of the tides. 

The dii anence at the moon's mean distance n 

.-be; - he proportion being as 121 

is lo U h 

III. It onlv remains on this subject, that Ian- 

swei : - the c series which I may be abbe tc antici- 

X 

1. Why i ane nc fide in lake and ponds ? 

An :. There arc n j waters that can flow into 
them^ without wi thei If the water will : 

imperceptibly il. I v -the- fthe 

water is more cor: ;: in I kes and ponds at the 
tin the m .: $ the meridian b 

above and b the n, bul avexi 

it b - in bun bed miles. 

%, Some have inc lined why the rise or swell ol 
r is b . . -• *-*. 



88 THE EBBING AND FLOWING OF THE SEA* 

Answer. The swell takes place at sea, and might 
be perceived if the depth could be exactly sounded 
at the time of high and low water; but where 
sounding is impracticable the difference cannot be 
perceived. 

3. Perhaps some may ask why there is no cur- 
rent in the ocean, as the waters rise and fall ; as 
there is in the mouths of creeks and rivers. 

Answer. Where waters are deep, but a small 
motion is necessary in order for such a swell to rise 
or to subside, because such a multitude of particles 
will move a little. If a spoonful of water be taken 
out of a pailful, no current will be produced in or- 
der to till up the hollow which it occasioned. The 
hollow or cavity will be filled partly from the ad- 
jacent surface, but more by the rising of the water 
immediately below, which will be forced upwards 
by the weight of the surrounding waters. If in the 
middle of the Pacific Ocean, an aqueous segment 
of the terraqueous globe of an hundred feet depth in 
the centre should be taken off; although this would 
occasion no real concavity, yet there would be a 
kind of comparative concavity with respect to the 
convexity of the water level ; so that if it could re- 
main in this situation, although it would be a per- 
fect plane of 24 miles, 4 furlongs and 70 poles in 
diameter, without the least concavity, yet it would 
be down hill, as we term it, from the circumference 
to the centre ; but this hollow would immediately 
fill up without occasioning airy perceptible current 
in the ocean. In the solid planet before supposed^ 
TWiose figure was a perfect sphere, the dispropor- 
tion between the attraction of the sun on its nearest 
and farthest parts, and the velocity of those part?, 



THE ESEIXG A::B FLOWING OF THE SEA. 89 

Would have no visible effect ; but It would occasion 
a something like the hollow wi biotit coneavitj just 

spoken of (shall I call it a convex concavity ?) on 
each side of the planet ; and these two places 
would be directly to and from the sun, whether the 
planet were in motion or at rest on its axis, for 
where no effect is produced no time is required. 
If the planet were aqueous there would be a swell 
■of water in each of these places : and if it revolved 
on its axis, the sinking of the waters in one place 
and their elevation in another would take place so 
praduabv that no current or commotion could be 
perceived. 

4. But here is another query. How can there 
. a tide on the side of the earth opposite the moon, 
stein? the earth does not move round the ibooq, 
and therefore can have no centrifugal three from it ? 
Answer. It is true that the earth does not move 
and the moon, hut it moves round the centre of 
vitv of the earth and mooiu waich is not tar 
the suriace of the earth, in a direct line exten- 
ig from the centre of the earth to that of the 
n. If the densities of the earth and the moon 
wsere eq ?T ai, then this centre of gravity would be 
e forty- i part- of the distance from the earth's 
tve in a direct line towards the centre of the 
toon. It is a point in this line where the two 
4obes would be exactly poised. Now as the earth 
Id ac pure a centrifugal force from this point, it 
. oalu he also from the moon, which is always in 
rr me dr- a. One body can never stand 
still with another revolving round it ; but both 
or move round their common centre of gravity. 
an is as r u . for the larger body 

U 2 



§0 THf] EBBING AND FLOWING ©F THE SEA* 

as for the smaller .one, and would originate if rt 
were not originally given. Where a primary plan- 
et has several moons, as Jupiter, Saturn and Hers- 
chel have, it must in its own motion have respect 
to each- of them, according to their distance and 
weight. This will cause its small motion round 
the centre of gravity to be very irregular, and also 
its tides. The same observation will also apply to 
the sun, surrounded by the primary planets, with 
respect to the irregularity of his motion around the 
centre of gravity of the system, and of the ebbings 
and Sowings of his lucid atmosphere, or whatever it 
he (if fluid) which surrounds his body. 

There are no other questions which I can at 
present conceive of, excepting those of a local na- 
ture, or such as arise from the effects of local cir- 
cumstances, and have no concern in the general 
theory. Ssch is the inquiry which I have frequent- 
ly heard respecting the remarkably high tides ob- 
served at the Bay of Fundy. There is no doubt 
but the true cause of this and other irregularities of 
a like nature might be discovered by a particular 
investigation of- local circumstances. 

Thus we have seen, in the course of this disser- 
tation on the causes of the tides, that they are occa- 
sioned by a disproportion between the motion of 
the earth and the distance of some parts of it from 
the sun or the moon, the centre only beino at the 
distance which its motion requires. We have seen 
that the centripetal force preponderates on the side 
of the earth next the sun or moon, on account of its 
proximity ; and that there is a preponderance in 
favour of the centrifugal force on the opposite side 
of .the earth, on account of its greater distance 

i 
# 



THE MOTION AND VELOCITY OP LIGHT. 91 

-which would require a slower motion. We have 
seta that -water,- being fluid, will be affected by this 
disproportion, and become elevated on the two op- 
posite sides of the earth, towards and from the moon 
or the sun ; and that by the revolution of the earth 
on her axis, we meet both these elevations of the 
water, and the depressions which must necessarily 
occupy the intermedium, once in each Lunar day. 
We have seen then as clearly the reason of two 
ebbs and flows In a Lunar day as of one. 

Before I dismiss this subject I would observe, 
that the great irregularities in the motion and dis- 
tance of the moon, together with the variations of 
the winds, and a variety of local circumstances, 
conspire to irregulate the tides, both with respect 
to their time and degree. 

' II. The method by which the motion of Light 
has been discovered, and its velocity determined, 
was to be explained. 

The motion of light, and the velocity of it, have 
been discovered by the eclipses of the satellites or 
moons of Jupiter. The number of these satellites 
is four. The revolution of the first, or nearest to 
Jupiter, is performed in 1 day, 18 hours, 2y min- 
utes and 33 seconds $ that of the second, in 3 days, 
13 hours, 13 minutes and 42 seconds ; that of the 
third, in 7 days, 3 hours, 42 minutes and 33 se- 
conds 5 and that of the fourth, or outermost, in 16 
days, 16 hours, 32 minutes and 8 seconds. Their 
orbits are nearlv circular, and therefore their mo- 
tlons nearly uniform. The orbits of the three first 
are so nearly in the plane of Jupiter's orbit that 
they fall into his shadow at every full and are eclip- 
sed. The fourth is so far distant; and makes se> 



92 THE MOTION AND VELOCITY OP LIGHT. 

great an angle with the plane of Jupiter s orbit that 
it does not fall into his shadow when the sun is 
more than sixty degrees from its nodes. There 
are generally about thirty eclipses in every month, 
counting those of all the satellites together. They 
are of use in determining the longitude of places on 
the land, and would be of great advantage at sea, 
if the irregular and violent motions of a ship did 
not prevent the observation of them. 

In the calculation of these eclipses, after apply* 
ing every equation which could possibly arise from 
the inequality of the motions of the respective 
moons, and of Jupiter, the calculated time would 
frequently differ several minutes from the observed 
time. .Sometimes it would be too early, sometimes 
too late, and sometimes it would agree with obser- 
vation. This difference could not arise from the 
motions of the satellites, because it was found to be 
the same at the same time with regard to everv one 
oitnem. If at a certain time the eclipses of one 
satellite were found to take place either earlier or 
later than the calculated time, or to agree with cal- 
culation ; the case would be found to be the same 
with respect to all the rest of the satellites. Besides 
all their eclipses were observed to take place before 
the calculated time in a certain part of their orbits, 
where at another time they took place after it. 

But it was observed at length that their eclipses 
always took place earlier, with respect to the cal- 
culated time, when Jupiter was at or near his op- 
position to the sun, and later when he was near his 
conjunction with the sun. This circumstance 
made it evident that the difference was only occa- 
sioned by the motion of light. Jupiter is nearer 



HIE CONSISTENCY &€, $8- 

the earth at the time of his. opposition than at the 
time of his conjunction, by the whole diameter of 
the earth's orbit, or 190 million miles. In the for- 
mer circumstance the eclipses were observed earlier 
because light jjaving less distance to travel, arri- 
ved sooner : lrHhe latter case, light, having a great- 
er distance to My, the eclipses were consequently 
observed some minutes later. The greatest differ- 
ence was found to be 8 minutes and 15 seconds* 
earlier in one case, and so much later in the other ; 
so that light travels 190 millions of miles in 16 
minutes and 30 seconds, which is at the rate of 
H 1,515,151 miles in one minute, or 191,919 miles 
in a second of time. This is 1,439,393 times the 
velocity of a cannon ball. 

Ill/ Before I conclude I must, according to what 
was proposed, show the consistency of the motion 
of a planet or cornet in an eccentric or elliptical 

orbit. 

The consistency of such a motion necessarily 
results from the combined effect of the laws of na- 
ture ; which laws have been discovered, and^by 
which we explain the phenomena of nature;, but 
how or why those laws must necessarily exist xan 
never be explained. No man can explain to us 
what gravitation is, any farther than that it is a ten- 
dency of bodies towards each other 5 or why the 
law of continued motion is, in the nature of things, 
necessary. Their necessity in order to prevent 
universal confusion is evident, and their existence 
any man may prove. Their effects are visible 
throughout the Solar system, as well as in all the 
scenes through which we pass on earth. These 
-ate the primary laws of nature. The former § 



5H TRE CONSISTENCY 0? 

generally called the centripetal force, and the latter 
the centrifugal force, when speaking of the motions 
t?f planets in the system. 

From the combined effect of these primary laws 
two secondary laws arise, which Wve been men- 
tioned, and which are observable anions the plan- 
ets. Let us look at them again and see how far 
the province of each extends. 
^ 1. The squares of the periodical times of the 
different planets must be in the same proportion to 
each other as the cubes of their various distances 
are. 

2. If a line be conceived to join a planet, or a 
comet, and the sun, and to be carried round the sun 
by the comet or planet; such a line will describe 
or pass over the same quantity of area, in a o-iven 
time, in one part of the orbit as it will in another 
part : or in every part, like areas in like times. 

The former of these laws does not extend to the 
regulation of a certain planet's motion in various 
parts of its orbit, or there would be no need of the 
latter ; neither does the latter interfere in the adjust- 
ment of the mean motions of the various planets to 
their mean distances. 

Although the former of these secondary laws re- 
quires that the velocity of a planet at a greater dis- 
tance be less, yet it requires that the area descri- 
bed in a given time be greater • because a planet 
four times as far from the sun as another, must ev- 
idently describe sixteen times the area in one revo- 
lution, and has but eight times as long to perform 
a revolution in (as you will find by calculation) and 
therefore must describe double the area in a riven 
time, b 



AN ECCENTRIC MOTION. 95 

A planet then in its perihelium moves with 
greater velocity than a planet would that should 
revolve in a circle at the same distance from the 
sun, because it describes more area in a given time ; 
the area described by a certain planet being always 
equal, whether it move in a circle or an ellipsis^ 
and the quantity of area being greater with respect 
to a planet at a greater distance, or whose mean 
distance is greater. From a parity of argument 
also the velocity of a planet in its aphelion is less 
than that of one that should revolve in a circle at 
the same distance from the sun. 

The planet Mercury in its perihelium is only 
29-260,000 miles from the sun, in which circum- 
stance its hourly motion is 15 minutes and 51 se- 
conds. Now the centrifugal force, arising from so 
rapid a motion, overbalances the sun's attraction 
even at this small distance because a planet revol- 
ving in a circle at this distance would only move 
14 minutes and 27 seconds pier hour. When Mer- 
cury is at his mean distance nom the sun, which is 
3 6, 8 42 ,000 miles, his hourly motion is 10 minutes 
and 14 seconds, which would be the uniform mo- 
lion of a planet revolving at the same distance from 
the sun in a circle. But when Mercun is in aphe- 
lion, his distance from the sun is 44,430,000 miles, 
and his hourly motion only 6 minutes and 53 se- 
conds ; whereas a planet revolving at the same 
distance in a circle would move 7 minutes and 43 
seconds in an hour. His velocity therefore in his 
aphelion is not sufficient to balance the sun's 
attraction. 

Thus it appears evident that the preponderance 
of the centrifugal force ; when a planet is in its per- 



9o THE CONSISTENCY GP 

ihelium, will throw it off to its aphelion, from 
whence it will be drawn down again to its perihe- 
iium by the preponderance of gravity, or the sun's 
attraction. 

It may not be thoroughly understood by every 
one, perhaps, how the motion of a planet becomes 
so much accelerated in one part of its orbit, and 
retarded in the other part of it. In order to make 
this a little more plain to the understanding, I would 
observe that if a planet should revolve about the 
sunin,aiiue circle no such circumstance could 
take place ; because the direction of the planet's 
motion in every part of the orbit would be perpen- 
dicular to that of the sun's attraction, which could 
therefore neither impel nor impede the planet in its 
progress. But the motion of a pJa.net in an ellipti- 
cal orbit is perpendicular to the sun's attraction on- 
ly at its aphelion or perihelium. From aphelion 
to perihelium, the direction of its motion is a little 
inclining towards the sun, so that it will be contin- 
ually accelerated by the sun's attraction : but in 
passing from perihelium to aphelion the direction of 
a planets motion is just as much inclined from the 
sun, so that its velocity will be continually dimin- 
ished bv the sun's attraction. 

mi 

Finally, if the distance and velocity of a planet. 
or comet, be precise!}- adjusted to each other, and 
at the same time the direction of its motion be per- 
pendicular to the direction of the sun, it will forever 
revolve in a true circle with an uniform velocity ; 
but if otherwise in any respect, it will revolve for- 
ever in an orbit more or less eccentric, in such a 
manner that its mean distance and mean motion 
will perfectly correspond. It cannot fall to the 






AN ECCENTRIC MOTION. 9? 

sun, because as it approaches towards him ftscjgj 
trifugal farce will increase taster than the sun's at- 
traction 5 neither can it be thrown oh 1 from him 
beyond a certain distance, because in receding from 
Limits centrifugal forcewiil decrease faster than 
the attraction ofth^^tk/Lho^been abundantly 



proved from tl ioiw^WaR^^Thus then- 

it will vibrate, be -n fMe two .ijpjesi which act 
upon it, in a maim :.s natural ancFaj prjhen- 

sible/if we were^|pstomedto it, asfne| |joa 
of a pendulum. 

My exertions on this raarticular subject tsSRTbeeti 
augmented in con- ,, ^n'ce of having understood 
that -some persons were adopting the agency of 
electricity in order to explain the consistency plan 
eccentric motion; but as I have adva^^dnotwng 
of mere opinion or conjecture on tne subject ; 
nothing but facts which, admit of demonstration, I 
trust that all who have understood me are satisfied 
in this respect : for an explanation irom si; en prin- 
ciples must afuord satisfaction. 

I would iu :; serve farther that this vib 
of a planet up and down, with respect to its da 
from the sun, cannot be the combined e 
gravity and electricity; because if it were] 
mean distances of all the planets and comets from 
the sun would be the same. The eccentricities of 
their orbits might be various, but their mean dis- 
tances would all be equal, being tl it distance at 
which the power of gravity and electricity would 
be balanced. 





# 



* 



O 



) 




SUPPLEMENT, 



CONCERNING THE DENSITY OP THE PLANETS* 

HAVING said but little respecting the different 
densities of the various planets, in the course of the 
preceding lectures, I have allotted this subject a 
place here. 

We believe all matter to be equally heavy, or 
alike subject to the power of gravitation, with re- 
spect to reciprocal attraction ; so that when the dif- 
ference of bodies with regard to bulk, does not cor- 
respond to their difference in weighty we conclude 
that they vary in density ; that is, that one body 
contains more matter and another less, in any de- 
terminate bulk. Thus if a cubic inch of one kind 
of metal were as heavy as two cubic inches of a- 
nother kind, we should conclude that the inch of 
the one contained as much matter as the two inch^ 
es of the other ; or that the density of the former 
metal was double that of the latter. 

From this definition of the word density, it ap- 
pears to be the quotient arising from the division of 
the weight of a body by its solid contents ; and as 
the contents of globes are in exact proportion to the 
cubes of their diameters, the comparative density 
of a planet may be obtained by dividing its weight 
by the cube of its diameter. But we must come to 
the grand query, viz : In what manner are we t® 
determine the weight of a planet ? 

This subject, although at first view apparently 



100 SUPPLEMENT, 

buried in darkness, is not involved in impenetrable 
obscurity. We have shown, in the foregoing lec- 
tures, that there is a certain proportion existing be- 
tween the cubes of the distances of the primary 
planets and the squares of their respective revolu- 
tions ; and, with regard to any set of secondary 
planets, or satellites, we have also shown that there 
is a certain proportion between the cubes of their 
distances and the squares of *heir periods. This 
proportion varies with regard to the satellites of 
different primary planets, on account of the differ- 
ent weight of the respective primary. It is the 
weight, therefore, of a planet which determines the 
proportion between the cubes of the distances of 
its satellites raid the squares of their revolutions ; 
and consequently this proportion must determine 
the weight of a planet. Therefore, to determine 
the weight of the sun, divide the -cube of the dis- 
tance of either of the primary planets, by the square 
of its revolution ; and for the weight of a planet 
which has one or more satellites, divide, in like 
manner, the cube of the distance of the satellite, or 
either of them, by the square of its period, This 
will precisely determine the proportional weight of 
the sun, and of such primary planets as have satel- 
lites ; which being respectively divided by the cubes 
of their diameters, will give their relative densities. 
The weight of a solitary planet can only be com- 
puted, or rather conjectured, from its efiect in dis- 
turbing the motions of other planets. Perhaps it 
may be determined considerably near to the truth, 
hy comparing its effect in this way, with that of a 
planet whose weight is known, and making due al- 
lowance for the difference of their relative situa« 



SUPPLEMENT. 101 

iions. But tne weight, and consequently the den- 
sity of such planets, must remain rather uncertain, 
until physical astronomy is carried to greater per- 
fection. 

Concerning the Comets, 

Comets are opaque bodies, moving through the 
heavens in extremely eccentric orbits. Their or- 
bits are not situated all nearly in the same plane, 
like those of the planets, but are in almost every 
direction, and some of tl^em move from east to 
west. By reason of the very great eccentricity of 
their orbits, they can only be seen when near their 
perihelia. Their periods are so long, and they are 
so seldom seen, that it is difficult to determine the 
elements of their orbits, so as to predict their re- 
turns. On their returns they may not always be 
recognized; for the earth may be in a very clilTer- 
ent part of her orbit, which may give the comet a 
very different appearance. Records are kept, how- 
ever, of every appearance of a comet, and we know 
not at what degree of perfection this part of astron- 
omy may hereafter arrive. The comet which ap- 
peared in 1531, is supposed to be the same which 
afterward appeared in 1607, 1682 and 1759, com- 
pleting its period in about 76 years. It may there- 
fore be expected to return again in the year 1834 
or 1835. That of 1680 is the most remarkable of 
all the comets, and answers so well to the accounts 
of the one of 1 105, that it is believed to be the same, 
completing its period in about 575 years. By a ret- 
rogression of seven periods, we find that one return 
of this comet was about the time of the ilood* — 

I 2 



102 .SUPPLEMENT. 

Whether that return was on the very year of the 
deluge, cannot now be determined, ancient chro- 
nology not being sufficiently precise, and the peri- 
ods of comets also being liable to some variation, — 
.Ridiculous as the opinion may seem, this comet is 
supposed by some to have occasioned that mighty 
inundation. The distance of this comet from the 
sun's centre, when in its perihelium, is about 500 ? 
000 miles ; and when in its aphelion, it is about 
1 3,1 61 .500,000 miles. In the former case its velo- 
city is nearly 800,000 miles an hour, and inthelat^ 
ter it is only about 30 miles. 

A TABLE 
Showing the Diameters, Distances and Densities 
of the Primitive Planets. The Densities of 
Mercury , Venus and Mars are more doubtful 

Names of Diameters. Distances. Densi 

Planets. E. Miles." E. Miles. ties. 

The SUN 887,462 .25 

MERCURY 3^,222 36,841.949 204 

VENUS 7,690 68,841^587 127 

The EARTH 7,964 95,173^127 100 

MARS 5,150 145,054,515 73 

JUPITER 94,100 494,860,227 20 

SATURN 78,990 907,125,000 11 

HERSCHEL 25 ; 226 1,812,631,799 22 




SUPPLEMENT. 1>Q$ 

TABLES 

for Computing the TIME when the Stars come 

to the Meridian; and also when they 

Rise and Set 



TABLE L 
A CATALOGUE 

■Of the Names of the Principal Fixed Stars and 
of the Constellations in which they are situa- 
ted, together with the time of their passing 
the Meridian, on the last day of December, tW 
Third Year after Bissextile, and their Semidi- 
urnal Arcs ; fitted to Latitude 40 degrees and 
43 minutes North, and 74 degrees and 15 min- 
utes West Longitude from 'Greenwich; but null 
serve for New- Jersey and the adjacent parts of 
Neiv-York and Pennsylvania, loithout essential 
Variation, throughout the present Century. 

f£f= Mean Time, or such as is shown by a true 
Clock, is\ere reckoned; also the time of the 
Stars' coming to the Meridian is counted from 
$lidiiight. 

Stars of the First Magnitude, 



Names of 


Constel- 


On Merid. 


Arc. 


Stars, 


lations. 


H. M. S. 


H. M. EL 


Aldebaran 


Taurus 


21 4G 59 


6 56 36 


Altair 


Aqiiila 


13 4 47 


6 23 10 


Antares 


Scorpio 


9 41 46 


4 19 54 


Arcturus 


Bootes 


7 31 9 


7 12 19 


Betelouese 


Orion 


23 6 34 


6 24 29 


Capeila 


Auriga 


22 24 42 


9 57 se 



104 



SUPPLEMENT. 



TABLE I. Continued. 



Names of 
Stars. 

Castor 

Fomalhaut 

Procyon 

Regulus 

Rigel 

Sirius 

Spica 

Vega 

Stars 

Algenib 

Algol* 

Almaach 

Alphard 

Alpheratz 

Bellatrix 

Benetnach 

Deneb 

Dubhe 

Lesath 

Markab 

Menkar 

Mirach 

Pole Star 

Pollux 

Scheat 

Zubenelg 

Zubenesh 



Constel- 
lations. 

Gemini 
Pisces 
Little Dog 
Leo 
Orion 
Great Dog 
Virgo 
Lyra 



On Merid. 
H. M. S. 

47 56 
16 9 58 

54 39 
3 23 10 

22 27. 8 

23 58 12 
6 39 34 

11 53 47 



Art 

H. M. S. 

8 10 20 
3 57 13 
6 18 37 
6 44 8 
5 29 50 
5 11 
5 23 23 
8 52 16 



Leo 

Ursa Major 

Scorpio 

Pegasus 

Ceti 



49 13 
9 5 43 
9 16 33 
5 31 42 
7 48 11 

5 50 11 
Never sets- 

6 54 20 



of the Second Magnitude. 

Pegasus 17 26 2 6 

Persejis 20 18 7 

AncUomeda 19 14 41 

Hydra 2 43 13 

Andromeda 17 21 11 

Orion 22 36 39 

Ursa Major 7 4 11 

5 3 58 

4 16 47 Never sets. 
10 44 35 3 18 
16 18 3 6 49 23 
20 14 29 6 10 39 

Andromeda 18 21 37* 8 24 49 

Ursa Minor 18 18 38 Never sets. 

Gemini 59 4 7 49 52 

Pegasus 16 17 18 7 43 20 

Libra 8 30 52 5 28 42 

Libra 8 4 33 5 4 44 



* This is a very variable star. It is sometimes 
no larger than one of the first magnitude. 



SUPPLEMENT. 



105 



TABLE I. Continued. 



Stars 

Names of 
Stars. 
Acubens 
Albirco 
Alcyone 
Alderaimin 
Algorab 
Allioth 
Kochab 
Rastaben 
Schedar 
Sednus 
Vindemiatrix 



of the Third Magnitude. 



Constel- 
lations, 
Caneer 

Cygni 

Pleiades 

Cephei 

Corvi 

Ursa Major 

Ursa Minor 

Draco 

Cassiopeia 

Bootes 

Virgo 

TABLE II. 



On Mend. 
H. M. S. 



2 
12 
20 
14 

$ 

6 



13 
17 

19 



Arc 
H. M. So 

6 43 2 

7 2 10 
7 26 55 

45 Never sets, 

35 4 59 55 

Never sets, 

8 14 50 Never sets, 

11 15 27 Never sets. 

17 52 21 Never sets, 

7 48 28 8 56 

6 17 7 6 40 46 



13 
46 
58 
36 
30 
10 



The Acceleration of the Stars for every Month 
throughout Four Years, commencing with 

Bissextile. 

First after Bissextile. 
H. M. S* 



January 
February 
March 
April 
May 
June 
July 
August 
September 
October 
November 
December 



Bissextile. 

H. M. S. 
o' 

2 1 53 

3 55 54 

5 57 47 
7 55 44 

9 57 37 
11 55 35 

13 57 28 
15 59 21 
17 57 18 
19 59 11 
21 57 8 



January 

February 

March 

April 

May 

June 

July 

August 

September 

October 

November 

December 



2 57 

2 4 50 

3 54 55 
5 56 48 
7 54 45 
9 56 39 

11 54 36 
13 56 29 
15 58 22 
17 56 19 
19 58 12 
21 56 9 



SOS 



SUPPLEMENT. 



TABLE II. Continued. 



Second after Bissextile. 
H. M. S. 



January 

February 

March 

April 

May 

June 

July 

August 

September 

October 

•November 

December 



1 58 

2 3 51 

3 53 56 
5 55 49 
7 53 46 
9 55 40 

11 53 37 
13 55 30 
15 57 23 
17 55 20 
19 57 13 
21 55 10 



Third after 

January 

February 

March 

April 

May 

June 

July 

August 

September 

October 

November 

December 



Bissextile. 
H. M. S. 

59 

2 2 5% 

3 52 57 
5 54 50 
7 52 48 
9 54 41 

11 52 38 
13 54 31 
15 56 24 
17 54 21 
19 56 14 
21 54 11 



TABLE III. 



The Acceleration of the Stars for Day*. 



1 

2 
3 
4 
5 
6 

7 

8 

9 
10 



M.. S. 



C/3 



3 56 


11 


7 52 


12 


11 48 


13 


15 44 


14 


19 40 


15 


23 35 


16 


27 31 


17 


31 27 


18 


35 23 


19 


39 19 


20 



i. 


M. 


S. 





43 


15 





47 


11 





51 


7 


55 


3 





58 


59 


1 


2 


54 


1 


6 50 


1 


10 46 


1 


14 


42 


1 


18 


38 



21 



22 

23 

24 

25: 

26 

27| 
28 

29 
30 



1 
1 
1 
1 
1 
1 
1 
1 
1 
1 



M. S. 

22 34 
26 30 
30 26 
34 22 
38 18 



42 
46 
50 
54 



13 

9 
5 
1 



31 Days— 2 H. 1 M. 53 S* 



57 57 






STOPLEMENT. 107 

DIRECTIONS 

por finding the time when the stars come to the 
meridian; or what is called their southing , if 
they pass south of the zenith. 

1. Take out the time when they are on the me- 
ridian, given in table f . 

2. Find whether the given year be Bissextile, or 
the first, second or third after it. This you may do 
by dividing the date by four ; if nothing remain it is 
Bissextile, and the remainder, if any, will point out 
the year after Bissextile. With this and the month, 
take the acceleration out of table II. and subtract it 
from the former time. 

3. With the day of the month, take the accele- 
ration out of table III. and subtract it from the for- 
mer remainder. 

Note. — Borrow 24 hours whenever there shall 
be occasion ; but if you borrow, in the course of the 
operation, remember to take out the acceleration 
for one day more than the given day of the month* 

EXAMPLE. 

What time will Alcyone (the brightest star in the 
Pleiades, or seven stars) south on the 19th of De- 
cember, 1822 ? 

H. M. S. 
Alcyone on Mer. from Table I. 20 58 19 
Second after Bissextile, December, 21 55 10 

Having borrowed I say 20th day 

Throw off the forenoon hours, 

Alcyone south ia the evening, at >9 44 SI 



23 
1 


3 9 
18 38 


21 
12 


44 31 
00 00 



IDS SUPPLEMENT. 

DIRECTIONS 

Tor finding the rising and setting of Stars* 

First find their time of southing, or coming to the 
meridian, as above ; then, for the rising, subtract the 
Semidiurnal Arc, found in Table [. or add it to find 
the setting. Note. — If you borrow 24 hours in 
subtracting, you will have the time of rising the pre- 
ceding day, and must yet subtract the acceleration 
for one day 5 in order to obtain the rising on the giv- 
en day ; or if, after adding, the hours exceed 24,. 
you will have the time of setting on the following* 
day, and must add the acceleration for. one day, to 
bring it back to the given day. 

EXAMPLE. 

What time will Aldebaran set on the first day of 
February, 1833, which will be the first year after 
Bissextile ? 

Aldebaran on mer. from Table I. 
First after Bissextile, February, 

First day of the month 

Southing, 
Semidiurnal Arc, add 

Rejecting 24 hours, 
Acceleration for one day, add 

Sets in the .morning, at 2 38 45 

FINIS* 



H. 


M. 


s. 


21 


46 


59 


2 


4 


50 


19 42 


9 


' 


3 


55 


19 


38 


13 


6 


56 


36 


2 


34 


49 




3 


56 



r 






1 



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i/'S 



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Will 

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